Подготовительные шаги

# Установим рабочую директорию
setwd("~/Documents/GitHub/RProjects_EF/Networks")
# Подгрузим необходимые для дальнейшего анализа библиотеки
## install.packages("igraph")
## install.packages("igraphdata")
## install.packages("ggraph")
## install.packages("tidygraph")
## install.packages("DescTools")


library(igraph);

Присоединяю пакет: ‘igraph’

Следующие объекты скрыты от ‘package:stats’:

    decompose, spectrum

Следующий объект скрыт от ‘package:base’:

    union
library(igraphdata);
library(ggraph);
Загрузка требуемого пакета: ggplot2
library(tidygraph);

Присоединяю пакет: ‘tidygraph’

Следующий объект скрыт от ‘package:igraph’:

    groups

Следующий объект скрыт от ‘package:stats’:

    filter
library(DescTools);
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

Присоединяю пакет: ‘DescTools’

Следующий объект скрыт от ‘package:igraph’:

    %c%

Обработка данных и создание графа

# Загрузим данные для исследования: набор ребер и вершин
edges <- read.csv("edges_1.csv", header=T) 
colnames(edges) <- c('from', 'to', 'type1', 'type2', 'weight')

nodes <- unique(edges[c('from', 'type1')])
more_nodes <- unique(edges[c('to', 'type2')])

colnames(nodes) <- c('organisation', 'type')
colnames(more_nodes) <- c('organisation', 'type')

nodes <- rbind(nodes, more_nodes)
nodes <- unique(nodes[c('organisation', 'type')])
rownames(nodes) <- NULL
edges <- edges[c('from', 'to', 'weight')]

# Создадим также набор обратных величин для весов ребер (это пригодится нам в дальнейшем). Исходные веса нам уже не понадобятся
edges$weight <- 1 / edges$weight

net <- graph_from_data_frame(d=edges, vertices=nodes, directed=F)

V(net)$color <- ifelse( V(net)$type=="Business Enterprise", "red", 
  ifelse( V(net)$type=="Private not for profit", "purple", 
    ifelse( V(net)$type=="Government", "green", 
      ifelse( V(net)$type=="Higher Education", "blue", "black") 
    ) 
  ) 
)
head(V(net)$color, 10)
 [1] "red"    "red"    "red"    "red"    "red"    "red"    "purple" "green"  "purple" "red"   

Поясним, почему в дальнейшем будем работать именно с обратными весами: Кратчайший путь и кратчайшее расстояние в данной задаче будут представлять собой не то же самое, что и в задаче с издержками перевозок или длинами расстояний между вершинами в качестве весов ребер. Отрицательные веса мы не используем, потому что алгоритм Дейкстры работает с неотрицательными весами ребер, поэтому далее мы оперируем с обратными весами, т.к., на наш взгляд, этот выбор является наиболее оптимальным для преодоления возникших трудностей.


Исследовательский вопрос

Исследовательский вопрос: Какие есть способы улучшения взаимодействия учреждений высшего образования Новой Зеландии (если это вообще требуется)?

Наше исследование показывает, что возможно повысить эффективность небольших университетов посредством увеличения сотрудничества с крупными, которые в свою очередь имеют тесное сотредничество с бизнесом.

Детали см. в Задании 6.


Анализ датасета

Описание датасета

Датасет представляет из себя множество вершин с качественными характеристиками и множество ребер с числовыми характеристиками (весами).

Вершинами являются организации Новой Зеландии, которые занимаются написанием научных статей в качестве одного из видов деятельности. Качественной характеристикой вершин является вид организации (государственная организации, высшее учебное заведение, коммерческое предприятие и частное некоммерческое предприятие). Всего в датасете 1511 вершин.

Между i-ой и j-ой вершинами (организациями) существует ребро, если за период 2010-2015 гг. на Scopus была опубликована хотя бы одна статья, хотя бы один автор которой числится в организации i, а другой автор – в организации j. Всего в датасете 4273 ребра.

Вес ребра равен количеству совместных опубликованных научных работ. Если вес ребра между i-ой и j-ой вершиной равен 3, то это означает, что за указанный период на Scopus было опубликовано 3 научные работы, у которых хотя бы один автор числится в организации i, а другой — в организации j.


Задание 2

При использовании нескольких пакетов для работы с графами не оказалось возможным интерпретируемо визуализировать граф полностью. Поэтому для отображения структуры нашей сети найдем 100 самых центральных по степени вершин и представим связи между ними при помощи пакета ggraph.

V(net)$degrees <- degree(net)
nodes$degrees <- V(net)$degrees

for_vis_n <- nodes[order(-nodes$degrees),][1:100, 1:2]
for_vis_e <- edges[(edges$from %in% for_vis_n$organisation & edges$to %in% for_vis_n$organisation),]

for_vis_net <- graph_from_data_frame(d=for_vis_e, vertices=for_vis_n, directed=F)
V(for_vis_net)$degrees <- degree(for_vis_net)

for_vis_net %>%
  ggraph(layout='graphopt') +
  geom_node_point(aes(color = type, size=round(degrees/20))) +
  geom_edge_link(alpha = 0.05) +
  theme_void() +
  ggtitle("Network of New Zealand organisations")

Как можно увидеть, среди 100 самых центральных вершин с количественной точки зрения преобладают организации государственного сектора, однако самыми крупными здесь являются новозеландские университеты. Первые 5 мест по числу совместных научных работ принадлежат именно им, лидером по данному показателю является Университет Окленда, самый крупный и престижный университет Новой Зеландии.

Рассчитаем базовые параметры нашего графа. Так как весами дуг в данном случае является число совместных работ, то есть “сила связи” двух вершин, будем использовать обратные веса для подсчета центральностей через кратчайшие пути. Это довольно разумно, так как от написания дополнительной общей работы прирост в силе связи двух организаций должен монотонно снижаться, как и разница в пути до соседа.

#Считаем базовые параметры графа

# Density
# The proportion of present edges from all possible ties.
p <- edge_density(net)

# связность сети
no <- igraph::components(net)$no # в пакете statnet такое же название
csize <- igraph::components(net)$csize
csize
 [1] 1463    2    2    2    3    2    2    2    2    2    2    2    2    2    2    2    2    2    2    2
[21]    2    2    3    2
# Diameter (longest geodesic distance) (если несколько компонент, то диаметр самой большой)
# Note that edge weights are used by default, unless set to NA.
diam <- diameter(net, weights=NA)
diam_w <- diameter(net)
path <- get_diameter(net, weights=NA)
path_w <- get_diameter(net)
path
+ 7/1511 vertices, named, from 21a717d:
[1] Dairy Production Systems Ltd.  Straven Road Veterinary Centre AgResearch                    
[4] Auckland Council               Auckland District Health Board New Zealand National Eye Bank 
[7] Project Litefoot Trust        
path_w
+ 9/1511 vertices, named, from 21a717d:
[1] Dairy Production Systems Ltd.     Straven Road Veterinary Centre    AgResearch                       
[4] Massey University                 University of Auckland            Victoria University of Wellington
[7] GNS Science                       ECoast Limited                    Dumpark Data Science             
# рассчитаем кратчайшие пути
# Average path length 
# The mean of the shortest distance between each pair of nodes in the network 
# (in both directions for directed graphs). 
m_dist <- mean_distance(net, weights=NA)
m_dist_w <- mean_distance(net)

Плотность нашего графа составляет 0.0037. Такая низкая плотность (вероятность образования связи) довольно естественная для вероятности написания научной работы. Наша сеть имеет 24 компонент связности: одна главная, соединяющая практически все вершины, а все остальные имеют по 2-3 вершины. Диаметр (наибольший из кратчаших путей) имеет длину 4.01, или 6, если брать единичные веса для всех дуг.

Изучим соседство самой центральной вершины — Оклендского Университета (с кем чаще всего взаимодействует наиболее престижный ВУЗ страны):

# We can also easily identify the immediate neighbors of a vertex.
# The 'neighbors' function finds all nodes one step out from the focal actor.
# To find the neighbors for multiple nodes, use 'adjacent_vertices()'.
d <- data.frame(neighbors(net, V(net)["University of Auckland"], mode="total")$type)
groups <- as.data.frame(table(d))[, 2]
pie(groups, labels=paste0(as.data.frame(table(d))[, 1], ', ',round(groups/sum(groups)*100, digits=1), '%'), 
    col=c(5, 2, 3, 4), main='Neighbors of University of Auckland')

# To find node neighborhoods going more than one step out, use function 'ego()'
# with parameter 'order' set to the number of steps out to go from the focal node(s).
neigh2 <- data.frame(ego(net, order = 2, nodes = V(net)["University of Auckland"])[[1]]$type)
groups2 <- as.data.frame(table(neigh2))[, 2]
pie(groups2, labels=paste0(as.data.frame(table(neigh2))[, 1], ', ',round(groups2/sum(groups2)*100, digits=1), '%'), 
    col=c(5, 2, 3, 4), main='Two-step neighbors of University of Auckland')

Довольно ожидаемо, что чаще всего в написании научных работ такой успешный университет сотрудничает с индустрией. Это подтвеждает наше предположение о том, успех научной работы зависит от работы с бизнесом. В ближайшем окружении данной организации также принято вести исследования с индустрией.

Сравним нашу сеть с теоритическими моделями случайного графа на основе распределения числа их соседей, диаметра, среднего кратчайшего пути и числа компонент связности. Начнем с модели случайного графа Эрдеша-Реньи.

#Генерируем модели случайного графа erdos.renyi
p <- edge_density(net)

random_model <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))


gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 


diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 


number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)

Как можно заметить, все рассматриваемые показатели нашей сети значимо отличаются от модельных, значит, структуру нашей сети нельзя описать данным образом.

Обратимся к модели “Малого мира” с регулярной решеткой. Однако в этом случае сперва нужно подобрать гиперпараметр — долю переприсоединенных дуг.

#Генерируем модели случайного графа с регулярной решеткой
n_of_nei <- mean(degree(net))
diam_net <- diameter(net, weights=NA)
#Ищем оптимальное значение p
mean_dist_net <- mean_distance(net)
model <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
res <- rep(NA, 100)
for (i in 1:100){
  model[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = i/100)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

# p = 0.99

random_model <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
par(mfrow = c(1, 1))


gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 


diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 


number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)

# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
  model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

plot(x=c(1:40)/10, y=res)
#power=2.15

random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))

hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))


gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 


diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 


number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)

Аналогично предыдущему случаю, данная модель плохо описывает структуру нашего графа. Значимо совпадает лишь диаметр, так как по нему в том числе происходил подбор гиперпараметра.

Рассмотрим также схожесть с моделью Барабаши-Альберта, включающей предпочтительное присоединение к наиболее центральным вершинам.


# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
  model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

#power=2.15

random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))


gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 


diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 


number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)

Как мы получили, данная модель тоже не подходит для описания структуры новозеландской сети: все статистически значимо отличается, кроме параметра, по которому проходил подбор гиперпараметра.

Выводы

Выводы по Заданию 2: Ни одна из теоретических моделей, известных нам, не описывает структуры нашего графа достаточно точно.


Задание 3

В этом задании нам предлагается посчитать различные меры центральности вершин и сделать содержательные выводы на основе полученных расчетов.

Замечание

Для анализа используем обратные веса, т.к. их использование делает осмысленным расчет центральности по близости и кратчайшему пути, но не искажает остальных мер центральности вершин.

Центральность по степени

Для начала посчитаем центральность по степени:

deg <- degree(net)

# plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=deg)

Теперь построим гистограмму распределения степеней вершин:

# гистограмма степеней вершин
hist(deg, main="Histogram of node degree", breaks=50, prob=TRUE) 

# распределение степеней вершин

mean(deg) # Средняя степень вершины по графу
[1] 5.655857
# ~ 5.66
Mode(deg) # Модальная степень вершин графа
[1] 1
attr(,"freq")
[1] 599
# 1 -> 599 раз
median(deg) # Медиана степеней вершин
[1] 2
# ~ 2
top_10_degree <- tail(sort(deg), 10) # топ-10 по степеням
top_10_degree # в топе - 7 университетов, 3 гос. учреждения
 Canterbury District Health Board                        AgResearch             University of Waikato 
                              121                               126                               136 
   Auckland District Health Board                    AUT University Victoria University of Wellington 
                              143                               145                               204 
         University of Canterbury                 Massey University               University of Otago 
                              241                               310                               406 
           University of Auckland 
                              551 

Вывод: Центральность вершин по степени не зависит от весов. Подавляющее большинство вершин имеет степень, меньшую 50. Так, медиана кол-ва соседей равняется 2. В среднем у вершины такого графа степень равна 5.66. Наиболее часто встречающаяся степень вершины — 1, которая встречается 599 раз. Если мы посмотрим 10 вершин с наибольшим числом соседей, то окажется, что 7 из них являются университетами, в числе которых крупнейший — университет Окленда (степень вершины максимальная — 551). Оставшиеся 3 организации являются государственными: 2 департамента здравоохранения и 1 исследовательская компания. Степень у всех вершин, входящих в топ-10, > 100.

Центральность по близости

Далее рассчитаем центральность по близости двумя способами: В первом варианте все веса ребер графа являются 1, в другом используются обратные веса ребер.

clos1 <- closeness(net, weights=NA) # Первый способ - без учета весов
clos1
                                       45 South Management Ltd. 
                                                   0.0002281022 
                                                     Abacus ALS 
                                                   0.0002440810 
                                                 AbacusBio Ltd. 
                                                   0.0002704164 
                                              ABB Power Quality 
                                                   0.0002391772 
                            ABI Rehabilitation New Zealand Ltd. 
                                                   0.0002207506 
                                         AC Research Associates 
                                                   0.0002610285 
                            Academic Colleges Group New Zealand 
                                                   0.0002593361 
                              Accident Compensation Corporation 
                                                   0.0003096934 
                       Action on Smoking and Health New Zealand 
                                                   0.0002593361 
                                                  Active Health 
                                                   0.0002492522 
                                      Acurity Health Group ltd. 
                                                   0.0002918856 
                                                Ade Consultants 
                                                   0.0002593361 
                                         Adidas Sports Medicine 
                                                   0.0002593361 
                                        Adis International Ltd. 
                                                   0.0002604167 
                                Advanced Clinical Skills Centre 
                                                   0.0002619859 
                                                          AECOM 
                                                   0.0002700513 
                                                      AECS Ltd. 
                                                   0.0002308403 
                                                  Aerocool Ltd. 
                                                   0.0002308403 
                                                  Aeroqual Ltd. 
                                                   0.0002739726 
                                              Affinity Services 
                                                   0.0002593361 
                                        AFT Pharmaceuticals Ltd 
                                                   0.0002771619 
                                             AFTpharmaceuticals 
                                                   0.0002593361 
                                  Agencies for Nutrition Action 
                                                   0.0002492522 
                                Agile Utilities New Zealand Ltd 
                                                   0.0002430134 
                                               Agknowledge Ltd. 
                                                   0.0002332634 
                                                     AgResearch 
                                                   0.0003456619 
                                             Agri-Optic NZ Ltd. 
                                                   0.0002430134 
                                             Agribusiness Group 
                                                   0.0002535497 
                                    AgriGenesis Biosciences Ltd 
                                                   0.0002348520 
                                          AgriHealth NZ Limited 
                                                   0.0001987281 
                                        Agrimm Technologies Ltd 
                                                   0.0002269117 
                                                AgriNova NZ Ltd 
                                                   0.0002281022 
                                            AgriQuality Limited 
                                                   0.0002280502 
                                         Agvance Marketing Ltd. 
                                                   0.0002474023 
                                                Air New Zealand 
                                                   0.0002797985 
                                               Air Quality Ltd. 
                                                   0.0002594034 
                                            Airborne Honey Ltd. 
                                                   0.0002393490 
                                          Akaroa Medical Centre 
                                                   0.0002491901 
  Ako Aotearoa National Centre for Tertiary Teaching Excellence 
                                                   0.0002359604 
                              Akoranga Integrated Health Clinic 
                                                   0.0002324500 
                                       Alan Bell and Associates 
                                                   0.0002256827 
                       Albany Basin Accident and Medical Centre 
                                                   0.0002186270 
                        Alcohol Advisory Council of New Zealand 
                                                   0.0002121791 
                       Alcohol Harm Minimisation Advisory Group 
                                                   0.0002508151 
                                      Alcohol Healthwatch Trust 
                                                   0.0002593361 
                                           Alexandra Lions Club 
                                                   0.0002283105 
                                       Alexandra Medical Centre 
                                                   0.0002491901 
                                              Alfriston College 
                                                   0.0002308403 
                                           All Seasons Pharmacy 
                                                   0.0002593361 
                               Allan Planning and Research Ltd. 
                                                   0.0002278423 
      Allen & Clarke  Policy and Regulatory Specialists Limited 
                                                   0.0002774695 
                                                      Alphalabs 
                                                   0.0002338087 
                         Alpine and Polar Processes Consultancy 
                                                   0.0002491281 
                                           Alzheimers Northland 
                                                   1.0000000000 
                        Amalgamates Solutions and Research Ltd. 
                                                   0.0002352941 
                                            Amity Health Centre 
                                                   0.0002491901 
                                        Ancare New Zealand Ltd. 
                                                   0.0002491901 
                                          Ancare Scientific Ltd 
                                                   0.0002702703 
                                                      Anexa FVC 
                                                   0.0002800336 
                                Anglesea Medical Properties Ltd 
                                                   0.0002653224 
                                          Animal Dermatology NZ 
                                                   0.0002305741 
                                Animal Health Board New Zealand 
                                                   0.0002381519 
         Animals and Marine Surveillance and Investigation Team 
                                                   0.0002430134 
                                     Animation Research Limited 
                                                   0.0002491901 
                                       Antarctic Heritage Trust 
                                                   0.0002308403 
                                         Antarctica New Zelaand 
                                                   0.0002686728 
                                  Antarctica Scientific Limited 
                                                   0.0002307337 
                                     Antipodean Pharmaceuticals 
                                                   0.0002547122 
                                    Aorangi Veterinary Services 
                                                   0.0002072968 
                                           Aotea Pathology Ltd. 
                                                   0.0002942042 
               Aotearoa Alcohol and Other Drug Consumer Network 
                                                   0.0002755580 
                                                AP EnerTec Ltd. 
                                                   1.0000000000 
                              Applied Engineering Research Ltd. 
                                                   0.0002252760 
                         Applied Research and Technologies Ltd. 
                                                   0.0002282584 
                        Applied Research Associates New Zealand 
                                                   0.0002268088 
                                       AquaBio Consultants Ltd. 
                                                   0.0002308936 
                                        Aquaculture New Zealand 
                                                   0.0002572016 
                                         Aqualinc Research Ltd. 
                                                   0.0002802691 
                                        Aquanet Consulting Ltd. 
                                                   0.0002430134 
                                Aquatic Research Solutions Ltd. 
                                                   0.0002434867 
                                             Aranui High School 
                                                   0.0002283626 
                                                  ARANZ Geo Ltd 
                                                   0.0002268088 
                                         ARANZ Medical Scanning 
                                                   0.0002392917 
                                                 Areograph Ltd. 
                                                   0.0002590003 
                                               ARH Construction 
                                                   0.0002593361 
                                                Aroa Biosurgery 
                                                   0.0002988643 
                                               Arohanui Hospice 
                                                   0.0002156102 
                                        Arotec Diagnostics Ltd. 
                                                   0.0002423068 
                                              Ascot Angiography 
                                                   0.0002369107 
                     Ascot Women's Cancer Centre of New Zealand 
                                                   0.0001984127 
                                    Asia New Zealand Foundation 
                                                   0.0002672368 
                                       Asphalt Products Limited 
                                                   0.0002391772 
                                Aspiring Veterinary Service Ltd 
                                                   0.0002431907 
                    ASR Limited Martine Consulting and Research 
                                                   0.0002367985 
                                     Assa Abloy New Zealand Ltd 
                                                   0.0002491901 
                                      Assistive Technology Ltd. 
                                                   0.0002430134 
                                        Assurity Consulting Ltd 
                                                   0.0002324500 
                                                   AsureQuality 
                                                   0.0002543882 
                                              AsureQuality Ltd. 
                                                   0.0002782415 
                                                    At the Vets 
                                                   0.0002436054 
                                 Atkinson and Rapley Consulting 
                                                   0.0002430134 
                                            Atlantis HealthCare 
                                                   0.0002593361 
                         Auckland-Waikato Fish and Game Council 
                                                   0.0002359604 
                                  Auckland Astronomical Society 
                                                   0.0002602811 
                                       Auckland Botanic Gardens 
                                                   0.0002511301 
                                         Auckland Breast Centre 
                                                   0.0002186270 
                                          Auckland City Mission 
                                                   0.0002802691 
                                 Auckland Clinical Studies Ltd. 
                                                   0.0002756340 
                                               Auckland Council 
                                                   0.0003233107 
                                      Auckland Cricket Assn Inc 
                                                   0.0002324500 
                                           Auckland Dermatology 
                                                   0.0002207506 
                                 Auckland District Health Board 
                                                   0.0003390980 
                                                   Auckland Eye 
                                                   0.0002627430 
                                           Auckland Heart Group 
                                                   0.0002635046 
                                  Auckland Institute of Studies 
                                                   0.0002328289 
                         Auckland International Airport Limited 
                                                   0.0002324500 
                                                Auckland Museum 
                                                   0.0003101737 
                           Auckland Refugee Community Coalition 
                                                   0.0002593361 
                                      Auckland Regional Council 
                                                   0.0002593361 
                         Auckland Southern Cross Hospital Group 
                                                   0.0002602134 
                                             Auckland Transport 
                                                   0.0002593361 
                                                   Auckland Zoo 
                                                   0.0003030303 
                                                        Aurecon 
                                                   0.0002764722 
            Australian and New Zealand College of Anaesthetists 
                                                   0.0002619859 
                                                 AUT University 
                                                   0.0003519887 
                                          Automation Design Ltd 
                                                   0.0001975114 
               Aviation Industry Association of New Zealand Inc 
                                                   1.0000000000 
                                                     Avivet Ltd 
                                                   0.0002474023 
                                       Avocado Industry Council 
                                                   0.0002280502 
                                        Babbage Consulting Ltd. 
                                                   0.0002734482 
                                Ballance Agri-Nutrients Limited 
                                                   0.0002676660 
                                               Bank of Scotland 
                                                   0.0002593361 
                                              Bartonk Solutions 
                                                   0.0002284148 
                                 Batten Animal Research Network 
                                                   0.0002525890 
                                      Baxter Healthcare Limited 
                                                   0.0002792516 
                                                  Bay Audiology 
                                                   0.0002391772 
                            Bay of Plenty District Health Board 
                                                   0.0003058104 
                                      Bay of Plenty Polytechnic 
                                                   0.0003003003 
                                 Bay of Plenty Regional Council 
                                                   0.0002537427 
                                                    Bay Urology 
                                                   0.0002297266 
                                  Bayer CropScience New Zealand 
                                                   0.0002270663 
                                      Bayleys Property Services 
                                                   0.0002593361 
                                             BC Consulting Ltd. 
                                                   0.0002278943 
                                            BCRL Energy Limited 
                                                   0.0001912046 
                                                           Beca 
                                                   0.0002905288 
                                      Beef and Lamb New Zealand 
                                                   0.0002886836 
                                             Bennett Scientific 
                                                   0.0002646203 
                                           Benthic Science Ltd. 
                                                   0.0002522068 
                                                 Berryworld Ltd 
                                                   0.0002322880 
                                  Best Practice Advocacy Centre 
                                                   0.0002754821 
                                                 Beta Solutions 
                                                   0.0002724796 
                                                  Bethesda Care 
                                                   0.0002602134 
                                        Betta Bees Research Ltd 
                                                   0.0002491901 
                                      Better Border Biosecurity 
                                                   0.0002321802 
                                      BHU Future Farming Centre 
                                                   0.0002425418 
                                       Bickler Consultants Ltd. 
                                                   0.0002793296 
                                                         BikeNZ 
                                                   0.0002391772 
                                          Bio Soil and Crop Ltd 
                                                   0.5000000000 
                                Bioactives Research New Zealand 
                                                   0.0002885170 
                                  Biodiscovery New Zealand Ltd. 
                                                   0.0002746498 
                                                 Biomarine Ltd. 
                                                   0.0002593361 
                                                Biomatters Ltd. 
                                                   0.0002754821 
                                         Biometrics Matters Ltd 
                                                   0.0002634352 
                                         Biopolymer Network Ltd 
                                                   0.0002813731 
                                        Biosecurity New Zealand 
                                                   0.0002486944 
                                BioSylve Forest Science NZ Ltd. 
                                                   0.0002252760 
                              BirdLife Global Seabird Programme 
                                                   0.0002228164 
                                               Blind Foundation 
                                                   0.0002430134 
                                         BLIS Technologies Ltd. 
                                                   0.0002650411 
                                     Blue Water Marine Research 
                                                   0.0002626050 
                                               Blues Rugby Club 
                                                   1.0000000000 
                                             Bodeker Scientific 
                                                   0.0002665245 
                                            Body Aid Clinic Ltd 
                                                   0.0002491901 
                                              Boffa Miskell Ltd 
                                                   0.0002977963 
                                         Bomac Laboratories Ltd 
                                                   0.0002773925 
                                              Boulcott Hospital 
                                                   0.0002111932 
                                               Braemar Hospital 
                                                   0.0002508781 
                                                     BRANZ Ltd. 
                                                   0.0003087373 
                                       Bream Bay Medical Centre 
                                                   0.0002593361 
                             Breast Care and Screening Services 
                                                   0.0002599428 
                        Breast Surgeons' Society of New Zealand 
                                                   0.0002593361 
                                               Breen Consulting 
                                                   0.0002308936 
                   Brian Ricketts Geological Consulting Limited 
                                                   0.0002227668 
                                        Broadway Medical Centre 
                                                   0.0002600104 
                                       Broadway Surgical Clinic 
                                                   0.0002237136 
                                           Broken Hills Gold Co 
                                                   0.0002593361 
                                          Brownrigg Agriculture 
                                                   0.0002231147 
                                  Bruce Shallard and Associates 
                                                   1.0000000000 
                                             Bunnythorpe School 
                                                   0.0002283105 
                                   Cadwallader Tree Consultancy 
                                                   0.0002391772 
                                         Cahill Animal Hospital 
                                                   0.0002430134 
                                     CAL Engineering Management 
                                                   0.0002282584 
                                           Callaghan Innovation 
                                                   0.0003299241 
                                               Cambridge Clinic 
                                                   0.0002533570 
                                  Cambridge Veterinary Services 
                                                   0.0002305741 
                                         Cameron Medical Clinic 
                                                   0.0002563445 
                                   Campbell and Associates Ltd. 
                                                   0.0002280502 
                          Cancer Control Council of New Zealand 
                                                   0.0002642008 
                                  Cancer Society of New Zealand 
                                                   0.0002883506 
                              Canterbury Charity Hospital Trust 
                                                   0.0002591345 
        Canterbury Civil Defence and Emergency Management Group 
                                                   0.0002288853 
                               Canterbury District Health Board 
                                                   0.0003436426 
                       Canterbury Earthquake Recovery Authority 
                                                   0.0002574665 
                                          Canterbury Health Ltd 
                                                   0.0002845760 
                                     Canterbury Medical Imaging 
                                                   0.0002428953 
                                              Canterbury Museum 
                                                   0.0003173596 
                  Canterbury Rugby Football Union and Crusaders 
                                                   0.0002275313 
                                      CanZealand Geoscience Ltd 
                                                   0.0002267060 
              Cape Kidnappers and Ocean Beach Wildlife Preserve 
                                                   0.0002594034 
                                                 Cape Sanctuary 
                                                   0.0002618487 
                        Capital and Coast District Health Board 
                                                   0.0003237294 
                                        Capital Eye Specialists 
                                                   0.0002218279 
                                               Capital Research 
                                                   0.0002500000 
                                             Carbon Partnership 
                                                   0.0002283105 
                                Cardiac Inherited Disease Group 
                                                   0.0002619859 
                                    Care of Orca Research Trust 
                                                   0.0001794044 
                                          Carey Baptist College 
                                                   0.0002593361 
                                         Carroll Consulting ltd 
                                                   0.0002442599 
                                         Carson Associates Ltd. 
                                                   0.0002252760 
                                        Carter Holt Harvey Ltd. 
                                                   0.0002748008 
                                    Carter National Observatory 
                                                   0.0002467308 
                                                Cashmere Health 
                                                   0.0002492522 
                                                     Catch Ltd. 
                                                   0.0002593361 
                                                         Catmed 
                                                   0.0002246686 
                                             Cawthron Institute 
                                                   0.0003321156 
                                    CBG Health Research Limited 
                                                   0.0002783964 
                                              Centennial Health 
                                                   0.0002493144 
                               Center for Backyard Astrophysics 
                                                   0.0002040816 
          Central and Southern New Zealand Craniofacial Program 
                                                   0.0002564103 
                                              Central City Vets 
                                                   0.0002430724 
                                          Central Otago Tourism 
                                                   0.0002491901 
                                         Central Stories Museum 
                                                   0.0002283105 
                                                     CentralMed 
                                                   0.0002816108 
                               Centre for Backyard Astrophysics 
                                                   0.0002906132 
            Centre for Clinical Research and Effective Practice 
                                                   0.0002699055 
                                    Centre for Dairy Excellence 
                                                   0.0002430724 
              Centre for Minerals Environmental Research (CMER) 
                                                   0.0002493766 
           Centre for Research Evaluation and Social Assessment 
                                                   0.0002128112 
                      Centre for Youth Health in South Auckland 
                                                   0.0002600104 
                                              CH and Associates 
                                                   0.0002352388 
                                     ChangeMakers Refugee Forum 
                                                   1.0000000000 
                                    Chatham Rock Phosphate Ltd. 
                                                   1.0000000000 
                                              Chemipreneur Ltd. 
                                                   0.0002529084 
                                       Chemistry Communications 
                                                   0.0002602134 
                                   Chiefs Super Rugby Franchise 
                                                   0.0002493766 
                                         Child and Youth Health 
                                                   0.0002621232 
                                     Child Poverty Action Group 
                                                   0.0002593361 
                                     Chilton Saint James School 
                                                   1.0000000000 
                                                   Chiptech Ltd 
                                                   0.0002492522 
                                      Christchurch City Council 
                                                   0.0002902758 
                         Christchurch Emergency Care Foundation 
                                                   0.0002899391 
               Christchurch Polytechnic Institute of Technology 
                                                   0.0003150599 
                             Christchurch Psychologists' Office 
                                                   0.0002590003 
                                    Christchurch Vascular Group 
                                                   0.0002606882 
                                                  City Care Ltd 
                                                   0.0002391772 
                                                   City Fitness 
                                                   0.0002640613 
                                       Civil Aviation Authority 
                                                   0.0002724796 
                                                          Claro 
                                                   0.0002593361 
                                     ClearSight Consultants Ltd 
                                                   0.0002686006 
                                     Clement and Associates Ltd 
                                                   0.0002300966 
                    Clendon Burns and Park Consulting Engineers 
                                                   0.0002273761 
                                               CLIMsystems Ltd. 
                                                   0.0002308403 
                                              Clinical Horizons 
                                                   0.0002494388 
                                               Clinical Systems 
                                                   0.0002207506 
                                  Clutha Veterinary Association 
                                                   0.0002500625 
                                        Coast and Catchment Ltd 
                                                   0.0002648305 
                                   Coast to Coast Health Centre 
                                                   0.0002186270 
                                Coastal and Aquatic Systems Ltd 
                                                   0.0002657454 
                                      Coastal Systems (NZ) Ltd. 
                                                   0.0002066543 
                                          Coastline Consultants 
                                                   0.0002252760 
                                    Cognition Education Limited 
                                                   0.0002593361 
                                                       Cognosco 
                                                   0.0002478929 
                                          Colgate-Palmolive Ltd 
                                                   0.0002391772 
                                           Colin Christian Ltd. 
                                                   0.0002491901 
                                          Collins Carriers Ltd. 
                                                   0.0002269117 
                                                 Colmar Brunton 
                                                   0.0002593361 
                                                Columba College 
                                                   0.0002491901 
                                              Common Ground Ltd 
                                                   0.0002328831 
                                       Commtest Instruments Ltd 
                                                   0.0002391772 
           Community Clinic for Sexual Health and Contraception 
                                                   0.0002593361 
                                  Compac Sorting Equipment Ltd. 
                                                   0.0002638522 
                                            Compac Technologies 
                                                   0.0002430134 
                                                 Compass Health 
                                                   0.0002542588 
                                  Compusoft Engineering Limited 
                                                   0.0002593361 
                                     Compusoft Engineering Ltd. 
                                                   0.0002594034 
                                             Comtel System Ltd. 
                                                   0.0002431315 
                                       Comvita New Zealand Ltd. 
                                                   0.0002774695 
                                           Connectos Consulting 
                                                   0.0002633658 
                                               Connovation Ltd. 
                                                   0.0002780095 
                      Conservation and Environmental Management 
                                                   0.0002364066 
                                   Construction Techniques Ltd. 
                                                   0.0002685285 
                                     Consulting Dietitians Ltd. 
                                                   0.0002619859 
                                            Contact Energy Ltd. 
                                                   0.0002635046 
                                        Contract Landscapes Ltd 
                                                   0.0002066543 
                                            CORE Education Ltd. 
                                                   0.0002635046 
                                                       Cosgrove 
                                                   0.0002391772 
                         Counties Manukau District Health Board 
                                                   0.0003258390 
                                                      Covec Ltd 
                                                   0.0002781641 
                                           CPG New Zealand Ltd. 
                                                   0.0002430134 
                                        Crawford Medical Centre 
                                                   0.0002594034 
                                                CRL Energy Ltd. 
                                                   0.0002653224 
                                               Cromwell College 
                                                   0.0002359604 
                                         Cropmark Seeds Limited 
                                                   0.0002369668 
                                   Crown Fibre Holdings Limited 
                                                   1.0000000000 
                                CURT St George's Medical Centre 
                                                   0.0002783964 
                                       Cuttriss Consultants Ltd 
                                                   0.0002267060 
                                        Cymbiotix Group Limited 
                                                   0.0002632272 
                                                    Cyperus Ltd 
                                                   0.0002825657 
                                         Dairy Consultants Ltd. 
                                                   0.0002070822 
                              Dairy Goat Co-operative (NZ) Ltd. 
                                                   0.0002693240 
                                  Dairy Production Systems Ltd. 
                                                   0.0001720282 
                                                        DairyNZ 
                                                   0.0003213368 
                                    David Butler Associates Ltd 
                                                   0.0002430134 
                                    Davidson Environmental Ltd. 
                                                   0.0002702703 
                                                 DaVinci Clinic 
                                                   0.0001838573 
                                       DCM Process Control Ltd. 
                                                   0.0002593361 
                             DEA Research Software Surgery Ltd. 
                                                   0.0002593361 
                                            Deepwater Group Ltd 
                                                   0.0002300966 
                                                         DeerNZ 
                                                   0.0002280502 
                                                       Deloitte 
                                                   0.0002950723 
                                     Department of Conservation 
                                                   0.0003377237 
                                      Department of Corrections 
                                                   0.0002391772 
                                             Development Action 
                                                   0.0002359604 
                                          Development By Design 
                                                   0.0002359604 
                                           Devon Medical Centre 
                                                   0.0002157032 
                                      DHI Water and Environment 
                                                   0.0002039152 
                                             Diabetes Otago Inc 
                                                   0.0002491901 
                                          Diagnostic Laboratory 
                                                   0.0002626050 
                                              Diagnostic Medlab 
                                                   0.0002792516 
                                      Digestive Health Services 
                                                   0.0002507523 
                                        Digital Sensing Limited 
                                                   0.0002658161 
                                             Disability Connect 
                                                   0.0002594034 
                                     Disability Resource Centre 
                                                   0.0002633658 
                                                   Diversity NZ 
                                                   0.0002633658 
                                                 DM Consultants 
                                                   0.0002746498 
                                           DNA Investments Ltd. 
                                                   0.0002227171 
                          Dnature diagnostics and research Ltd. 
                                                   0.0002640613 
                                  Doctors for Sexual Abuse Care 
                                                   0.0002461841 
                                            Donaghys Industries 
                                                   0.0002281022 
                                       Donald Beasley Institute 
                                                   0.0002765487 
                                    Dorothy-Jean and Associates 
                                                   0.0002270148 
                                                  Dovedale Ltd. 
                                                   0.0002884338 
                                       Downer EDI Works Limited 
                                                   0.0002273244 
                                      Dr. Malcolm McKellar Ltd. 
                                                   0.0001973165 
                                                 Dragonfly Ltd. 
                                                   0.0002623295 
                            Drummond Food Science Advisory Ltd. 
                                                   0.0002491901 
                                           Dumpark Data Science 
                                                   0.0001706193 
                                               Duncan Cotterill 
                                                   0.0002493144 
                                           Dunedin City Council 
                                                   0.0002493766 
                                     Dunedin Heat Pumps Limited 
                                                   0.0002491901 
                                Dunedin South Veterinary Clinic 
                                                   0.0002430134 
                              Dunning Thornton Consultants Ltd. 
                                                   0.0002596728 
                                          Dynamic Controls Ltd. 
                                                   0.0002450380 
                                                       Dynatest 
                                                   0.0002597403 
                         Dyspraxia Support Group of New Zealand 
                                                   0.0002507523 
                                          Earthquake Commission 
                                                   0.0002746498 
                                   Earthtech Consulting Limited 
                                                   0.0002594034 
                                Eastern Institute of Technology 
                                                   0.0003043214 
                                   Eastern Region Fish and Game 
                                                   0.0002347969 
              Eastern Suburbs Association Football Club (ESAFC) 
                                                   0.0002724796 
                              Eastland Veterinary Services Ltd. 
                                                   0.0002436054 
                                       Eaton Power Quality Ltd. 
                                                   0.0002391772 
                                                ECG Consultants 
                                                   0.0002430134 
                        Eco-Vista Photography and Research Ltd. 
                                                   0.0002871088 
                                                 Eco Nomos Ltd. 
                                                   0.0002340824 
                                    Eco Research Associates Ltd 
                                                   0.0002837684 
                                                 ECoast Limited 
                                                   0.0002272727 
                                      EcoGecko Consultants Ltd. 
                                                   0.0002612330 
                                     Ecosynergy Group Ltd (EGL) 
                                                   0.0002359604 
                                                      Ectus Ltd 
                                                   0.0002308403 
                           Edmund Lawler and Associates Limited 
                                                   0.0002359604 
                                                Education House 
                                                   1.0000000000 
                                        Education Review Office 
                                                   0.0002593361 
                                 Educational Leadership Project 
                                                   0.0002308403 
                                          Electricity Authority 
                                                   0.0002740477 
                    Eli Lilly and Company (New Zealand) Limited 
                                                   0.0002595380 
                                           Elmwood Orthopaedics 
                                                   0.0002492522 
                            Eltham District Veterinary Services 
                                                   0.0002456399 
                                             Endoscopy Auckland 
                                                   0.0002594034 
                   Energy Efficiency and Conservation Authority 
                                                   0.0002693966 
                                 Energy Solution Providers Ltd. 
                                                   0.0002269117 
                                                    EnForm Tech 
                                                   0.0002297794 
                                         Enigma Publishing Ltd. 
                                                   0.0002600780 
                                                      Ensys Ltd 
                                                   0.0002391772 
                                                   Entecol Ltd. 
                                                   0.0002748763 
                                     Enviro-Mark Solutions Ltd. 
                                                   0.0002391772 
                                                Enviro Research 
                                                   0.0002297266 
                                         Environment Canterbury 
                                                   0.0003033060 
                          Environment Protection Authority(EPA) 
                                                   0.0002476474 
                              Environmental Management Services 
                                                   0.0002267060 
                                  Environmental Restoration Ltd 
                                                   0.0002252760 
                                    ENZO Nutraceuticals Limited 
                                                   0.0002508151 
                                                Epi-interactive 
                                                   0.0002658867 
                                     Epsom Girls Grammar School 
                                                   0.0002593361 
                                      Equine Health Association 
                                                   0.0002227171 
                                                    ERA Ecology 
                                                   0.0002635046 
                                                      Erin Park 
                                                   0.0002610285 
                                                            ESR 
                                                   0.0003396739 
                                            Etec Crop Solutions 
                                                   0.0002280502 
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                                  New Zealand Olympic Committee 
                                                   0.0002491901 
            New Zealand Organisation for Rare Disorders (NZORD) 
                                                   0.0002491901 
                                         New Zealand Parliament 
                                                   0.0002359604 
                                             New Zealand Police 
                                                   0.0002896032 
                           New Zealand Qualifications Authority 
                                                   0.0002359604 
                                  New Zealand Refining Co. Ltd. 
                                                   0.0002391772 
                           New Zealand Rheumatology Association 
                                                   0.0002779322 
                                        New Zealand Rugby Union 
                                                   0.0002651113 
New Zealand School Acupuncture and Traditional Chinese Medicine 
                                                   0.0002391772 
                                    New Zealand School of Music 
                                                   0.0002359604 
                       New Zealand Seafood Industry Council Ltd 
                                                   0.0002296739 
         New Zealand Society for Earthquake Engineering (NZSEE) 
                                                   0.5000000000 
                                       New Zealand Spinal Trust 
                                                   0.0002507523 
                                   New Zealand Tertiary College 
                                                   0.0002632272 
                                    New Zealand Timberlands Ltd 
                                                   0.0001937609 
                                   New Zealand Transport Agency 
                                                   0.0002702703 
                                           New Zealand Treasury 
                                                   0.0002914602 
                          New Zealand Underwater Heritage Group 
                                                   0.0002308936 
                          New Zealand Veterinary Pathology Ltd. 
                                                   0.0002461841 
                                        New Zealand Winegrowers 
                                                   0.0002626050 
                                         Newman Energy Research 
                                                   0.0002391772 
                                         Newtown Medical Centre 
                                                   0.0002754821 
                                                 NextWindow Ltd 
                                                   0.0002754821 
                                             Ngati Porou Hauora 
                                                   0.0002594034 
                                 Ngati Whakaue Tribal Lands Inc 
                                                   0.0002252760 
                                                Nielsen Company 
                                                   0.0002595380 
                                   NIU Development Incorporated 
                                                   0.0002762431 
                                                           NIWA 
                                                   0.0003415301 
                                             Norske Skog Tasman 
                                                   0.0002593361 
                            North Canterbury Veterinary Clinics 
                                                   0.0002437241 
                                            North Shore Hospice 
                                                   0.0002656748 
                              North Shore International Academy 
                                                   0.0002477701 
                            Northcott Research Consultants Ltd. 
                                                   0.0002787068 
                                        Northern Cancer Network 
                                                   0.0002619859 
                                  Northern Region IDEA Services 
                                                   0.0002593361 
                                     Northern Regional Alliance 
                                                   0.0002286760 
                         Northern Southland Veterinary Services 
                                                   0.0002073828 
                                Northland District Health Board 
                                                   0.0002968240 
                                     Northland Regional Council 
                                                   0.0002797985 
                                                       NorthTec 
                                                   0.0002665245 
                                             Novare Design Ltd. 
                                                   0.0002391772 
                                                   Numcore Ltd. 
                                                   0.0002593361 
                                                   Numinos Ltd. 
                                                   0.0002593361 
                                        Nurse Maude Association 
                                                   0.0002613013 
                                      Nutrigenomics New Zealand 
                                                   0.0002964720 
                               Nutrition Society of New Zealand 
                                                   0.0002491901 
                                                 NZ Oil and Gas 
                                                   0.0002394636 
                                        NZ Parsa Tiling Limited 
                                                   0.0002391772 
                                              NZFOCUS (NZ) Ltd. 
                                                   0.0002593361 
                                                    NZX Limited 
                                                   0.0002593361 
                                    O'Kane Consultants (NZ) Ltd 
                                                   0.0002664535 
                                                Oamaru Hospital 
                                                   0.0002491901 
                                                  Odyssey House 
                                                   0.0002593361 
               Office of the Health and Disability Commissioner 
                                                   0.0002593361 
   Office of the Parliamentary Commissioner for the Environment 
                                                   0.0002556891 
                                           Omahu Urology Clinic 
                                                   0.0002500000 
                                           OMV New Zealand Ltd. 
                                                   0.0002619859 
                                          Oncology Surgery Ltd. 
                                                   0.0002628812 
                                Open Polytechnic of New Zealand 
                                                   0.0003099814 
                                          OPRA Consulting Group 
                                                   0.0002392917 
                                        Optimal Clinical Trials 
                                                   0.0002562788 
                             Opus International Consultants Ltd 
                                                   0.0002934272 
                                             Oracle New Zealand 
                                                   0.0002359604 
                                             Oral Health Centre 
                                                   0.0002532928 
                                              Orange Consulting 
                                                   0.0002491901 
                                                  Orb Solutions 
                                                   0.0002602134 
                                     Organ Donation New Zealand 
                                                   0.0002656748 
                                            Oritain Global Ltd. 
                                                   0.0002491901 
                          Ornithological Society of New Zealand 
                                                   0.0002663825 
                                          Orokonui Ecosanctuary 
                                                   0.0002560164 
                                                          OSPRI 
                                                   0.0002751032 
                                        Otago Community Hospice 
                                                   0.0002592017 
                       Otago Computational Modelling Group Ltd. 
                                                   0.0002789400 
                                   Otago Daily Times Collective 
                                                   0.0002491901 
                                        Otago Girls High School 
                                                   0.0002930832 
                                                   Otago Museum 
                                                   0.0002759382 
                                              Otago Polytechnic 
                                                   0.0003050641 
                                         Otago Regional Council 
                                                   0.0002437241 
                                                Otahuhu College 
                                                   0.0002763958 
                                           Otakaro Pathways Ltd 
                                                   0.0002356268 
                                      Otorohanga Dental Surgery 
                                                   0.0002491901 
                                                 OTRS Group Ltd 
                                                   0.0002607562 
                                     Outome Management Services 
                                                   0.0002593361 
                                       P.N. Plimmer and Associ. 
                                                   0.0002594034 
                                    PA Handford and Assoc. Ltd. 
                                                   0.0002255300 
                                                 Pacific Brands 
                                                   0.0002593361 
                                Pacific Edge Biotechnology Ltd. 
                                                   0.0002823264 
             Pacific Health Research and Development Foundation 
                                                   0.0002724796 
                                        Pacific Radiology Group 
                                                   0.0002905288 
           Pacific Women's Health Research and Development Unit 
                                                   0.0002627430 
                                       Pakuranga Medical Centre 
                                                   0.0002207993 
                                          Palaecol Research Ltd 
                                                   0.0002888504 
                                  Palmerston North City Council 
                                                   0.0002430724 
                                  Palmerston North City Library 
                                                   0.0002359604 
                                                   Pansophy Ltd 
                                                   0.0002328831 
                                   Papamoa Pines Medical Centre 
                                                   0.0002822467 
                                            Paraparaumu College 
                                                   0.0002692515 
                                                  Paric Limited 
                                                   0.0002593361 
                                        Parkinson's New Zealand 
                                                   0.0002593361 
                                      Parresia Research Limited 
                                                   0.0002593361 
                                           Parsons Brinckerhoff 
                                                   0.0002593361 
                                    Pasifika Horizon Healthcare 
                                                   0.0002593361 
                                   Pasifika Medical Association 
                                                   0.0002594707 
                                          Pasifika Research Ltd 
                                                   0.0002360718 
                                                        Pathlab 
                                                   0.0002513826 
                                                 Patients First 
                                                   0.0002494388 
                               Paton-Simpson Associates Limited 
                                                   0.0002540005 
                                   Pattle Delamore Partners Ltd 
                                                   0.0002392917 
                                             Pegasus Health Ltd 
                                                   0.0002843332 
                                       Penny and Associates Ltd 
                                                   0.0002613013 
              Perinatal and Maternal Mortality Review Committee 
                                                   0.0002777778 
                                  Petersgate Counselling Centre 
                                                   0.0002391772 
                                       PF Olsen and Company Ltd 
                                                   0.0002257846 
                                       PGG Wrightson Seeds Ltd. 
                                                   0.0002501251 
                                                        PHARMAC 
                                                   0.0002787845 
                                             Pharmaceuticol Ltd 
                                                   0.0002496879 
                                  Pharmacy Guild of New Zealand 
                                                   0.0002593361 
                                      PharmTech Service Limited 
                                                   0.0002765487 
                 Philosophy of Education Society of Australasia 
                                                   0.0002593361 
                                        Photonz Corporation Ltd 
                                                   0.0002593361 
                                                    Pictor Ltd. 
                                                   0.0002593361 
                                                Pingar Research 
                                                   0.0002308936 
                                             Pinnacle Group Ltd 
                                                   0.0002596728 
                                               PipeTechnologies 
                                                   0.0002596054 
                                           Pipfruit New Zealand 
                                                   0.0002507523 
                                       Planning Consultants Ltd 
                                                   0.0002635741 
                                        Plant and Food Research 
                                                   0.0003419973 
                              Plant Protection Chemistry NZ Ltd 
                                                   0.0002307870 
                                              PlusGroup Limited 
                                                   0.0002363507 
                                                Pohatu Penguins 
                                                   0.0002400384 
                                                Polybatics Ltd. 
                                                   0.0002508151 
                                           Porirua City Council 
                                                   0.0002491901 
                                      Ports of Auckland Limited 
                                                   0.0002594034 
                                          Positive Thinking Ltd 
                                                   0.0002593361 
                                             Possum Observatory 
                                                   0.0002906132 
                                  Potter Building Services Ltd. 
                                                   0.0002764722 
                                                  Power Co Ltd. 
                                                   0.0002593361 
                      Power Systems Consultants New Zealand Ltd 
                                                   0.0001976285 
                                              PowerbyProxi Ltd. 
                                                   0.0002593361 
                                        Powerhouse Ventures Ltd 
                                                   0.0002434867 
                                    Practitioners First Limited 
                                                   0.0002594707 
                             Presbyterian Church of New Zealand 
                                                   0.0002619859 
                                  PriceWaterhouse Coopers (PwC) 
                                                   0.0002849003 
                               Priestley Structural Engineering 
                                                   0.0002691790 
                                    Private Endodontic Practice 
                                                   0.0002491901 
                                         ProCare Health Limited 
                                                   0.0002638522 
                                    Prohealth Physiotherapy Ltd 
                                                   0.0002493144 
                                                   Promisia Ltd 
                                                   0.0002492522 
                          Proteus Wildlife Research Consultants 
                                                   0.0002568053 
                                          Psychological Service 
                                                   0.0002593361 
                                              Psychology Centre 
                                                   0.0002599428 
                                        Pultron Composites Ltd. 
                                                   0.0002336449 
                                                        Pyrotek 
                                                   0.0002403268 
                                                     Q-Bit Ltd. 
                                                   0.0002425418 
                                                      QE Health 
                                                   0.0002619859 
                                                     Qnique Ltd 
                                                   0.0002806624 
                                           QStar Solutions Ltd. 
                                                   0.0002396932 
                                                      Quadradix 
                                                   0.0002593361 
                                       Quay Park Medical Centre 
                                                   0.0002772387 
                                          Queens Academic Group 
                                                   0.0002593361 
                                     Quest Integrity Group Ltd. 
                                                   0.0002753304 
                                         Quigley and Watts Ltd. 
                                                   0.0002507523 
                                   Quin Environmentals(NZ) Ltd. 
                                                   0.0002545177 
                                 Quintessence Developments Ltd. 
                                                   0.0002393490 
                                                     Quit Group 
                                                   0.0002843332 
                                  Radiata Pine Breeding Company 
                                                   0.0002252760 
                                      Radio Spectrum Management 
                                                   0.0002466700 
                                                     Rakon Ltd. 
                                                   0.0002593361 
                                       Rangiora New Life School 
                                                   0.0002590003 
                        Rape Prevention Education-Whakatu Mauri 
                                                   0.0002762431 
                            Rauawaawa Kaumatua Charitable Trust 
                                                   0.0002759382 
                                Raukatauri Music Therapy Centre 
                                                   0.0002593361 
                                  Raukura Hauora O Tainui Trust 
                                                   0.0002492522 
                                       Rayonier New Zealand Ltd 
                                                   0.0002595380 
                              Refugees as Survivors New Zealand 
                                                   0.0002619859 
                                  Reid Construction Systems Ltd 
                                                   0.0002685285 
                                               Renewable Energy 
                                                   0.0002252760 
                                                       Repromed 
                                                   0.0002835271 
                                    Reserve Bank of New Zealand 
                                                   0.0002701243 
                                        Resilient Organisations 
                                                   0.0002685285 
                       Resource Teacher: Learning and Behaviour 
                                                   0.0002593361 
                                          Revolution Fibres Ltd 
                                                   0.0002783964 
                                               Riccarton Rotary 
                                                   1.0000000000 
                        Risk Strategies Research and Consulting 
                                                   0.0002399232 
                                             Rivuli Development 
                                                   0.0002308936 
                                                RML Engineering 
                                                   0.0002308403 
                                         Roche Products Limited 
                                                   0.0002619859 
                                            Rockwell Automation 
                                                   0.0002593361 
                                    Rolleston Veterinary Clinic 
                                                   0.0002693966 
                                  Ropata Village Medical Centre 
                                                   0.0002786291 
                                 Rotorua General Practice Group 
                                                   0.0002754821 
                                       Rowe Davies Research Ltd 
                                                   0.0002632272 
      Royal Australian and New Zealand College of Psychiatrists 
                                                   0.0002593361 
        Royal Forest and Bird Protection Society of New Zealand 
                                                   0.0002648305 
             Royal New Zealand College of General Practitioners 
                                                   0.0002836879 
                              Royal New Zealand Plunket Society 
                                                   0.0002912056 
                                   Royal Society of New Zealand 
                                                   0.0002820079 
                      Ruaimoko Productions and Consultancy Ltd. 
                                                   0.0002491901 
                                                     Rumenz Ltd 
                                                   0.0002603489 
                                                      RuralLink 
                                                   0.0002308403 
 [ reached getOption("max.print") -- omitted 511 entries ]
plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos1 * 50)

top_10_clos1 <- tail(sort(clos1), 10) 
# Вектор-топ 42 также будет единичным, а вот вектор-топ 43 уже нет
top_10_clos1
  Reveal Infrastructure Ltd.          Napier City Council   RATO Natural Health Clinic 
                           1                            1                            1 
Stahlton Engineered Concrete        Katipo Communications     Workwise Employment Ltd. 
                           1                            1                            1 
                  Northpower   New Zealand Stock Exchange           Real Time Genomics 
                           1                            1                            1 
    Rotary Club of Riccarton 
                           1 
bottom_10_clos1 <- head(sort(clos1), 10)
bottom_10_clos1
                                         Tauranga City Council 
                                                  0.0001571092 
                                        Project Litefoot Trust 
                                                  0.0001703868 
                                          Dumpark Data Science 
                                                  0.0001706193 
                                 Dairy Production Systems Ltd. 
                                                  0.0001720282 
                                 SciCon Scientific Consultants 
                                                  0.0001725923 
New Zealand Employment Service and Work and Income New Zealand 
                                                  0.0001773050 
                                               IWM Consultancy 
                                                  0.0001779676 
                                        PLANTwise Services Ltd 
                                                  0.0001779676 
                                   Care of Orca Research Trust 
                                                  0.0001794044 
                                    Southern Veterinary Centre 
                                                  0.0001818843 
clos1["University of Auckland"]
University of Auckland 
          0.0004175365 
clos2 <- closeness(net)
clos2
                                       45 South Management Ltd. 
                                                   0.0003943799 
                                                     Abacus ALS 
                                                   0.0003948148 
                                                 AbacusBio Ltd. 
                                                   0.0006961899 
                                              ABB Power Quality 
                                                   0.0006413412 
                            ABI Rehabilitation New Zealand Ltd. 
                                                   0.0003938669 
                                         AC Research Associates 
                                                   0.0005551376 
                            Academic Colleges Group New Zealand 
                                                   0.0005551376 
                              Accident Compensation Corporation 
                                                   0.0007801036 
                       Action on Smoking and Health New Zealand 
                                                   0.0007336460 
                                                  Active Health 
                                                   0.0003948964 
                                      Acurity Health Group ltd. 
                                                   0.0008104601 
                                                Ade Consultants 
                                                   0.0003949673 
                                         Adidas Sports Medicine 
                                                   0.0005551376 
                                        Adis International Ltd. 
                                                   0.0006422174 
                                Advanced Clinical Skills Centre 
                                                   0.0003949738 
                                                          AECOM 
                                                   0.0005553066 
                                                      AECS Ltd. 
                                                   0.0003939742 
                                                  Aerocool Ltd. 
                                                   0.0005531777 
                                                  Aeroqual Ltd. 
                                                   0.0006964490 
                                              Affinity Services 
                                                   0.0003949673 
                                        AFT Pharmaceuticals Ltd 
                                                   0.0006421838 
                                             AFTpharmaceuticals 
                                                   0.0003949673 
                                  Agencies for Nutrition Action 
                                                   0.0003950001 
                                Agile Utilities New Zealand Ltd 
                                                   0.0003947654 
                                               Agknowledge Ltd. 
                                                   0.0003942829 
                                                     AgResearch 
                                                   0.0009296380 
                                             Agri-Optic NZ Ltd. 
                                                   0.0003947654 
                                             Agribusiness Group 
                                                   0.0003948792 
                                    AgriGenesis Biosciences Ltd 
                                                   0.0003944997 
                                          AgriHealth NZ Limited 
                                                   0.0005811195 
                                        Agrimm Technologies Ltd 
                                                   0.0006911531 
                                                AgriNova NZ Ltd 
                                                   0.0005536711 
                                            AgriQuality Limited 
                                                   0.0005536711 
                                         Agvance Marketing Ltd. 
                                                   0.0005548064 
                                                Air New Zealand 
                                                   0.0007336460 
                                               Air Quality Ltd. 
                                                   0.0003950063 
                                            Airborne Honey Ltd. 
                                                   0.0003949205 
                                          Akaroa Medical Centre 
                                                   0.0003948441 
  Ako Aotearoa National Centre for Tertiary Teaching Excellence 
                                                   0.0006951944 
                              Akoranga Integrated Health Clinic 
                                                   0.0003945848 
                                       Alan Bell and Associates 
                                                   0.0003897638 
                       Albany Basin Accident and Medical Centre 
                                                   0.0003935895 
                        Alcohol Advisory Council of New Zealand 
                                                   0.0003867563 
                       Alcohol Harm Minimisation Advisory Group 
                                                   0.0007321787 
                                      Alcohol Healthwatch Trust 
                                                   0.0003949673 
                                           Alexandra Lions Club 
                                                   0.0003936698 
                                       Alexandra Medical Centre 
                                                   0.0003948441 
                                              Alfriston College 
                                                   0.0003939742 
                                           All Seasons Pharmacy 
                                                   0.0003949673 
                               Allan Planning and Research Ltd. 
                                                   0.0003934603 
      Allen & Clarke  Policy and Regulatory Specialists Limited 
                                                   0.0005550492 
                                                      Alphalabs 
                                                   0.0003942276 
                         Alpine and Polar Processes Consultancy 
                                                   0.0003948315 
                                           Alzheimers Northland 
                                                   1.0000000000 
                        Amalgamates Solutions and Research Ltd. 
                                                   0.0005533577 
                                            Amity Health Centre 
                                                   0.0003948441 
                                        Ancare New Zealand Ltd. 
                                                   0.0005548944 
                                          Ancare Scientific Ltd 
                                                   0.0007609563 
                                                      Anexa FVC 
                                                   0.0008104933 
                                Anglesea Medical Properties Ltd 
                                                   0.0005532196 
                                          Animal Dermatology NZ 
                                                   0.0003944603 
                                Animal Health Board New Zealand 
                                                   0.0005538036 
         Animals and Marine Surveillance and Investigation Team 
                                                   0.0003947654 
                                     Animation Research Limited 
                                                   0.0003948441 
                                       Antarctic Heritage Trust 
                                                   0.0003939742 
                                         Antarctica New Zelaand 
                                                   0.0005532774 
                                  Antarctica Scientific Limited 
                                                   0.0003937421 
                                     Antipodean Pharmaceuticals 
                                                   0.0003948640 
                                    Aorangi Veterinary Services 
                                                   0.0003782167 
                                           Aotea Pathology Ltd. 
                                                   0.0007333288 
               Aotearoa Alcohol and Other Drug Consumer Network 
                                                   0.0005553704 
                                                AP EnerTec Ltd. 
                                                   1.0000000000 
                              Applied Engineering Research Ltd. 
                                                   0.0003896193 
                         Applied Research and Technologies Ltd. 
                                                   0.0004701219 
                        Applied Research Associates New Zealand 
                                                   0.0003937088 
                                       AquaBio Consultants Ltd. 
                                                   0.0005460494 
                                        Aquaculture New Zealand 
                                                   0.0006274107 
                                         Aqualinc Research Ltd. 
                                                   0.0007917378 
                                        Aquanet Consulting Ltd. 
                                                   0.0003947654 
                                Aquatic Research Solutions Ltd. 
                                                   0.0006379371 
                                             Aranui High School 
                                                   0.0003937473 
                                                  ARANZ Geo Ltd 
                                                   0.0003937088 
                                         ARANZ Medical Scanning 
                                                   0.0005547135 
                                                 Areograph Ltd. 
                                                   0.0007600330 
                                               ARH Construction 
                                                   0.0003949673 
                                                Aroa Biosurgery 
                                                   0.0006413752 
                                               Arohanui Hospice 
                                                   0.0006666201 
                                        Arotec Diagnostics Ltd. 
                                                   0.0005536524 
                                              Ascot Angiography 
                                                   0.0003947988 
                     Ascot Women's Cancer Centre of New Zealand 
                                                   0.0003734750 
                                    Asia New Zealand Foundation 
                                                   0.0003951218 
                                       Asphalt Products Limited 
                                                   0.0005547135 
                                Aspiring Veterinary Service Ltd 
                                                   0.0003951294 
                    ASR Limited Martine Consulting and Research 
                                                   0.0003942151 
                                     Assa Abloy New Zealand Ltd 
                                                   0.0003948441 
                                      Assistive Technology Ltd. 
                                                   0.0003947654 
                                        Assurity Consulting Ltd 
                                                   0.0005543822 
                                                   AsureQuality 
                                                   0.0003949212 
                                              AsureQuality Ltd. 
                                                   0.0007970684 
                                                    At the Vets 
                                                   0.0005226062 
                                 Atkinson and Rapley Consulting 
                                                   0.0005547389 
                                            Atlantis HealthCare 
                                                   0.0003949673 
                         Auckland-Waikato Fish and Game Council 
                                                   0.0003946024 
                                  Auckland Astronomical Society 
                                                   0.0003950014 
                                       Auckland Botanic Gardens 
                                                   0.0003950034 
                                         Auckland Breast Centre 
                                                   0.0003935895 
                                          Auckland City Mission 
                                                   0.0003950891 
                                 Auckland Clinical Studies Ltd. 
                                                   0.0003953194 
                                               Auckland Council 
                                                   0.0008874012 
                                      Auckland Cricket Assn Inc 
                                                   0.0003945848 
                                           Auckland Dermatology 
                                                   0.0003938669 
                                 Auckland District Health Board 
                                                   0.0009326414 
                                                   Auckland Eye 
                                                   0.0003950182 
                                           Auckland Heart Group 
                                                   0.0006413449 
                                  Auckland Institute of Studies 
                                                   0.0003946231 
                         Auckland International Airport Limited 
                                                   0.0003945848 
                                                Auckland Museum 
                                                   0.0008683322 
                           Auckland Refugee Community Coalition 
                                                   0.0003949673 
                                      Auckland Regional Council 
                                                   0.0003949673 
                         Auckland Southern Cross Hospital Group 
                                                   0.0007815128 
                                             Auckland Transport 
                                                   0.0003949673 
                                                   Auckland Zoo 
                                                   0.0007292915 
                                                        Aurecon 
                                                   0.0007607093 
            Australian and New Zealand College of Anaesthetists 
                                                   0.0005551376 
                                                 AUT University 
                                                   0.0009316976 
                                          Automation Design Ltd 
                                                   0.0003823478 
               Aviation Industry Association of New Zealand Inc 
                                                   1.0000000000 
                                                     Avivet Ltd 
                                                   0.0005547389 
                                       Avocado Industry Council 
                                                   0.0003942244 
                                        Babbage Consulting Ltd. 
                                                   0.0006415123 
                                Ballance Agri-Nutrients Limited 
                                                   0.0007605800 
                                               Bank of Scotland 
                                                   0.0003949673 
                                              Bartonk Solutions 
                                                   0.0005525811 
                                 Batten Animal Research Network 
                                                   0.0005548944 
                                      Baxter Healthcare Limited 
                                                   0.0005551376 
                                                  Bay Audiology 
                                                   0.0006413412 
                            Bay of Plenty District Health Board 
                                                   0.0008771219 
                                      Bay of Plenty Polytechnic 
                                                   0.0008292245 
                                 Bay of Plenty Regional Council 
                                                   0.0007937374 
                                                    Bay Urology 
                                                   0.0003947619 
                                  Bayer CropScience New Zealand 
                                                   0.0003932645 
                                      Bayleys Property Services 
                                                   0.0003949673 
                                             BC Consulting Ltd. 
                                                   0.0007916542 
                                            BCRL Energy Limited 
                                                   0.0003682590 
                                                           Beca 
                                                   0.0007985413 
                                      Beef and Lamb New Zealand 
                                                   0.0003952621 
                                             Bennett Scientific 
                                                   0.0005548944 
                                           Benthic Science Ltd. 
                                                   0.0005548944 
                                                 Berryworld Ltd 
                                                   0.0005538244 
                                  Best Practice Advocacy Centre 
                                                   0.0007810309 
                                                 Beta Solutions 
                                                   0.0003950277 
                                                  Bethesda Care 
                                                   0.0005551376 
                                        Betta Bees Research Ltd 
                                                   0.0003948441 
                                      Better Border Biosecurity 
                                                   0.0003942993 
                                      BHU Future Farming Centre 
                                                   0.0003948009 
                                       Bickler Consultants Ltd. 
                                                   0.0006419082 
                                                         BikeNZ 
                                                   0.0003947526 
                                          Bio Soil and Crop Ltd 
                                                   1.2000000000 
                                Bioactives Research New Zealand 
                                                   0.0007980255 
                                  Biodiscovery New Zealand Ltd. 
                                                   0.0007608293 
                                                 Biomarine Ltd. 
                                                   0.0003949673 
                                                Biomatters Ltd. 
                                                   0.0005551376 
                                         Biometrics Matters Ltd 
                                                   0.0006940374 
                                         Biopolymer Network Ltd 
                                                   0.0006965300 
                                        Biosecurity New Zealand 
                                                   0.0003949899 
                                BioSylve Forest Science NZ Ltd. 
                                                   0.0003896193 
                              BirdLife Global Seabird Programme 
                                                   0.0003895611 
                                               Blind Foundation 
                                                   0.0003947654 
                                         BLIS Technologies Ltd. 
                                                   0.0007603725 
                                     Blue Water Marine Research 
                                                   0.0003949933 
                                               Blues Rugby Club 
                                                   2.0000000000 
                                             Bodeker Scientific 
                                                   0.0008045790 
                                            Body Aid Clinic Ltd 
                                                   0.0003948441 
                                              Boffa Miskell Ltd 
                                                   0.0006960747 
                                         Bomac Laboratories Ltd 
                                                   0.0005552922 
                                              Boulcott Hospital 
                                                   0.0003910446 
                                               Braemar Hospital 
                                                   0.0003950591 
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                                     ChangeMakers Refugee Forum 
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                    Clendon Burns and Park Consulting Engineers 
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                                Coastal and Aquatic Systems Ltd 
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                                                       Cognosco 
                                                   0.0006413752 
                                          Colgate-Palmolive Ltd 
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                                                 Colmar Brunton 
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                                     Compusoft Engineering Ltd. 
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                                               Connovation Ltd. 
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                                            CORE Education Ltd. 
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                         Counties Manukau District Health Board 
                                                   0.0009297184 
                                                      Covec Ltd 
                                                   0.0005518436 
                                           CPG New Zealand Ltd. 
                                                   0.0003947654 
                                        Crawford Medical Centre 
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                                                CRL Energy Ltd. 
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                                        Cymbiotix Group Limited 
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                                                    Cyperus Ltd 
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                                         Dairy Consultants Ltd. 
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                              Dairy Goat Co-operative (NZ) Ltd. 
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                                  Dairy Production Systems Ltd. 
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                                                        DairyNZ 
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                                    Davidson Environmental Ltd. 
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                                                 DaVinci Clinic 
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                                       DCM Process Control Ltd. 
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                             DEA Research Software Surgery Ltd. 
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                                                         DeerNZ 
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                                          Development By Design 
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                          Dnature diagnostics and research Ltd. 
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                                                  Dovedale Ltd. 
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                                       Downer EDI Works Limited 
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                                      Dr. Malcolm McKellar Ltd. 
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                                                 Dragonfly Ltd. 
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                                Dunedin South Veterinary Clinic 
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                              Dunning Thornton Consultants Ltd. 
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                                                   0.0006956607 
                                                       Dynatest 
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                         Dyspraxia Support Group of New Zealand 
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                                          Earthquake Commission 
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                                   Eastern Region Fish and Game 
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              Eastern Suburbs Association Football Club (ESAFC) 
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                                       Eaton Power Quality Ltd. 
                                                   0.0006956607 
                                                ECG Consultants 
                                                   0.0003947654 
                        Eco-Vista Photography and Research Ltd. 
                                                   0.0005554535 
                                                 Eco Nomos Ltd. 
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                                                 ECoast Limited 
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                                      EcoGecko Consultants Ltd. 
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                                                      Ectus Ltd 
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                           Edmund Lawler and Associates Limited 
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                                 Energy Solution Providers Ltd. 
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                                                    EnForm Tech 
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                                         Enigma Publishing Ltd. 
                                                   0.0003949858 
                                                      Ensys Ltd 
                                                   0.0005547135 
                                                   Entecol Ltd. 
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                                     Enviro-Mark Solutions Ltd. 
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                                                Enviro Research 
                                                   0.0003943704 
                                         Environment Canterbury 
                                                   0.0008329125 
                          Environment Protection Authority(EPA) 
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                                  Environmental Restoration Ltd 
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                                                Epi-interactive 
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                                      Equine Health Association 
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                                                    ERA Ecology 
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                                                      Erin Park 
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                                                     Explore NZ 
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                                                  Eye Institute 
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                                     Far North District Council 
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                                        Feilding Medical Centre 
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                                                       FEM Ltd. 
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                                       Fern Research Foundation 
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                              Fisher and Paykel Healthcare Ltd. 
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                        Fishing Vessel Management Services Ltd. 
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                                                  FMR GROUP LTD 
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                                                       Fonterra 
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                              Food and Bio-based Products Group 
                                                   0.0006399482 
                                          Food and Health Group 
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                                Foot Science International Ltd. 
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                            Forensic and Industrial Science Ltd 
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                                                Forest and Bird 
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                        Fox and Associates-Consulting Surveyors 
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                                        Fred Hollows Foundation 
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  Fresenius Medical Care Australia Pty Ltd (New Zealand Branch) 
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                                           Frontier Global Ltd. 
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                                              Fruitfed Supplies 
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                                          Fruition Horticulture 
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                                              FullSpectrum Ltd. 
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                                              Fulton Hogan Ltd. 
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                                        Future Forests Research 
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                                                   Future Steps 
                                                   0.0003950367 
                                            FuturebyDesign Ltd. 
                                                   0.0003951613 
                                                FutureMATH Ltd. 
                                                   0.0003647701 
                            Gallagher Animal Management Systems 
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                                              Gambling Helpline 
                                                   0.0003947959 
                 Genesis Research & Development Corporation Ltd 
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                                      Genetic Technologies Ltd. 
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                                               Gentrack Limited 
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                                                         GEOKEM 
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                                            Geoventures Limited 
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                                    GHD Centre Level Napier St. 
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                                                    GHD Limited 
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                             Gillies McIndoe Research Institute 
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                                      Gisborne District Council 
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                                                    GNS Science 
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                                Good Life Research Centre Trust 
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                                                         Google 
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                            Greater Wellington Regional Council 
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                                   Greenweaver Architecture Ltd 
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                                Greerton Early Childhood Centre 
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                                            Gribbles Veterinary 
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                                                   GroPlus Ltd. 
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                                               Growth Solutionz 
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                                    Guardian Health Care (Bupa) 
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                                                   Hally Labels 
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                                            Hamilton Eye Clinic 
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                        Hamilton Sacred Heart College for Girls 
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                                   Hamilton Veterinary Services 
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                                                   Hamilton Zoo 
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                                      Hapai Te Hauora Tapui Ltd 
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                        Harker Underground Construction Limited 
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                                   Hawke's Bay Regional Council 
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                                                  Hawkins Watts 
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                                                Health Alliance 
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                                           Health Care Aotearoa 
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                                        Health New Zealand Ltd. 
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                                Health Outcomes Associates Ltd. 
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                               Health Partners Consulting Group 
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                                        Health Promotion Agency 
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                           Health Quality and Safety Commission 
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                                       Healthscope Laboratories 
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                                                     HealthWEST 
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                         Heavy Engineering Research Association 
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                                                 Heinz Wattie's 
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                                                Heke Consulting 
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                              Helios Integrative Medical Centre 
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                                                       Hemptech 
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                            Hepatitis Foundation of New Zealand 
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                                     Herbert Morton Accountants 
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                                              Heretaunga Health 
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                            Heritage New Zealand Pouhere Taonga 
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                             High Performance Sport New Zealand 
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                                        Highnam Associates Ltd. 
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                                         Hill Laboratories Ltd. 
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                                             Hiway Geotechnical 
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                     HodderBalog Social and Scientific Research 
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                                                    Holcim (NZ) 
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                                         Holmes Fire and Safety 
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                                      Horizons Regional Council 
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                                  Horowhenua Community Practice 
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                                       Horowhenua Library Trust 
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                                                    Horteye Ltd 
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                                                       HortPlus 
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                                            Hospice New Zealand 
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                              Hospice Palliative Care Education 
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                                                Hospice Waikato 
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                                             Hot Solutions Ltd. 
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                                         Humes Pipeline Systems 
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                                          Huntly Community Link 
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                                             Hush Interiors Ltd 
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                              Hutt Valley District Health Board 
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                                             Hyland Consultants 
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                          Hyland Fatigue Earthquake Engineering 
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                                              Hyperbaric Health 
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                                                            IAG 
                                                   0.0003947526 
                              Ian Kusabs and Associates Limited 
                                                   0.0005532740 
                           Ian McLean Consultancy Services Ltd. 
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                                                  Ichthyo-niche 
                                                   0.0003949158 
                                                      IGENZ Ltd 
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                                                            ILR 
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                                   Immunisation Advisory Centre 
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                               Inclusive Education Action Group 
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                               Independent Petroleum Laboratory 
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                                       Indufor Asia-Pacific Ltd 
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                                                Infoics Limited 
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                                            Inform Planning Ltd 
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                               Infrastructure Decisions Limited 
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                                  Inglewood Veterinary Services 
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                                     Injury Prevention Aotearoa 
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                                                 Inland Revenue 
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                              Innate Immunotherapeutics Limited 
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                                            Innate therapeutics 
                                                   0.0003946024 
                                       Inner City Women's Group 
                                                   0.0003949673 
                                                Inner Zest Ltd. 
                                                   0.0003949673 
                                                 INR Online Ltd 
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                                       Insect Science Solutions 
                                                   0.0003943162 
                                                   Insights MSD 
                                                   0.0003708776 
                                                 Inspiring Ltd. 
                                                   0.0005552162 
              Institution of Professional Engineers New Zealand 
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                    Intellectual Property Office of New Zealand 
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                                Intensive Care Flight Paramedic 
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                                                   Interactionz 
                                                   0.0003939742 
                                                        InterAg 
                                                   0.0005538070 
               International Animal Welfare Consultants Limited 
                                                   0.0003947654 
                         International Earth Sciences IESE Ltd. 
                                                   0.0003950220 
                                  International Pacific College 
                                                   0.0005547389 
                International Student Ministries of New Zealand 
                                                   0.0003950001 
                                  International Telematics Ltd. 
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                                                      Interpine 
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                                         Interpine Forestry Ltd 
                                                   0.0005450014 
                            Intus Digestive and Colorectal Care 
                                                   0.0003948441 
                                             Invenco Group Ltd. 
                                                   0.0005551376 
                                      Investigation Geology Ltd 
                                                   0.0003949085 
                                                          IPENZ 
                                                   0.0005551376 
                                    Irrigation New Zealand Inc. 
                                                   0.0003944594 
                                                       Isolytix 
                                                   0.0003948441 
                                              IZON Science Ltd. 
                                                   0.0007324195 
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                                                  Power Co Ltd. 
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                        Rape Prevention Education-Whakatu Mauri 
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                              Refugees as Survivors New Zealand 
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                                                       Repromed 
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                                        Resilient Organisations 
                                                   0.0006413412 
                       Resource Teacher: Learning and Behaviour 
                                                   0.0003949673 
                                          Revolution Fibres Ltd 
                                                   0.0003950578 
                                               Riccarton Rotary 
                                                   1.0000000000 
                        Risk Strategies Research and Consulting 
                                                   0.0007330129 
                                             Rivuli Development 
                                                   0.0003940518 
                                                RML Engineering 
                                                   0.0003939742 
                                         Roche Products Limited 
                                                   0.0003949738 
                                            Rockwell Automation 
                                                   0.0003949673 
                                    Rolleston Veterinary Clinic 
                                                   0.0003950567 
                                  Ropata Village Medical Centre 
                                                   0.0006419231 
                                 Rotorua General Practice Group 
                                                   0.0003950071 
                                       Rowe Davies Research Ltd 
                                                   0.0006408984 
      Royal Australian and New Zealand College of Psychiatrists 
                                                   0.0003949673 
        Royal Forest and Bird Protection Society of New Zealand 
                                                   0.0006963278 
             Royal New Zealand College of General Practitioners 
                                                   0.0007336460 
                              Royal New Zealand Plunket Society 
                                                   0.0006955571 
                                   Royal Society of New Zealand 
                                                   0.0003950578 
                      Ruaimoko Productions and Consultancy Ltd. 
                                                   0.0005548944 
                                                     Rumenz Ltd 
                                                   0.0003949789 
                                                      RuralLink 
                                                   0.0003939742 
 [ reached getOption("max.print") -- omitted 511 entries ]
plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos2 * 50)

top_10_clos2 <- tail(sort(clos2), 10) 
top_10_clos2
  Workwise Employment Ltd.                 Northpower New Zealand Stock Exchange 
                       1.0                        1.0                        1.0 
        Real Time Genomics   Rotary Club of Riccarton      Bio Soil and Crop Ltd 
                       1.0                        1.0                        1.2 
           PollenPlus Ltd.               GroPlus Ltd.           Blues Rugby Club 
                       1.2                        1.5                        2.0 
         Highlanders Rugby 
                       2.0 
bottom_10_clos2 <- head(sort(clos2), 10)
bottom_10_clos2
                                          Dumpark Data Science 
                                                  0.0002501171 
                                 Dairy Production Systems Ltd. 
                                                  0.0002502698 
New Zealand Employment Service and Work and Income New Zealand 
                                                  0.0002504864 
                                        Project Litefoot Trust 
                                                  0.0002504870 
                                         Tauranga City Council 
                                                  0.0002955979 
                                                Port Otago Ltd 
                                                  0.0003060701 
                                                 Travel Clinic 
                                                  0.0003065386 
                                         Dobbie Engineers Ltd. 
                                                  0.0003069975 
                                        NZ Strong Construction 
                                                  0.0003069975 
                                     Pulp Mill Technical Group 
                                                  0.0003069975 
clos2["University of Auckland"]
University of Auckland 
          0.0009338331 

Вывод: В обоих случаях максимальная центральность вершин будет составлять 1. В нашем графе существует 21 пара вершин, которая связана лишь между собой и более ни с кем (из рассчета для графа с единичными весами ребер). Из них лишь 5 организаций работали совместно более 1 раза (из рассчета для графа с обратными весами). Топ-10 центральных вершин по близости и топ-10 по степени уже существенно различаются. Так, центральность по близости университета Окленда составит 4.1753653^{-4} в первом случае и 4.1753653^{-4}. Т.е. round(1 / clos1["University of Auckland"]) или round(1 / clos2["University of Auckland"]) — сумма длин всех путей от университета Окленда до любой другой вершины в зависимости от метода рассчета.

Центральность по кратчайшему пути

betw1 <- betweenness(net, weights=NA)
head(betw1)
           45 South Management Ltd.                          Abacus ALS 
                             0.0000                              0.0000 
                     AbacusBio Ltd.                   ABB Power Quality 
                           228.0179                              0.0000 
ABI Rehabilitation New Zealand Ltd.              AC Research Associates 
                             0.0000                              0.0000 
top_10_betw1 <- tail(sort(betw1), 10)
top_10_betw1
   Auckland District Health Board           Plant and Food Research                        AgResearch 
                         44138.73                          55148.49                          61204.78 
            University of Waikato                    AUT University Victoria University of Wellington 
                         62949.44                          64866.37                          84858.46 
         University of Canterbury                 Massey University               University of Otago 
                        130456.08                         194334.96                         231358.36 
           University of Auckland 
                        385421.47 
bottom_10_betw1 <- head(sort(betw1), 10)
bottom_10_betw1
                45 South Management Ltd.                               Abacus ALS 
                                       0                                        0 
                       ABB Power Quality      ABI Rehabilitation New Zealand Ltd. 
                                       0                                        0 
                  AC Research Associates      Academic Colleges Group New Zealand 
                                       0                                        0 
Action on Smoking and Health New Zealand                            Active Health 
                                       0                                        0 
                         Ade Consultants                   Adidas Sports Medicine 
                                       0                                        0 
betw1["University of Auckland"]
University of Auckland 
              385421.5 
betw2 <- betweenness(net)
head(betw2)
           45 South Management Ltd.                          Abacus ALS 
                                  0                                   0 
                     AbacusBio Ltd.                   ABB Power Quality 
                                  1                                   0 
ABI Rehabilitation New Zealand Ltd.              AC Research Associates 
                                  0                                   0 
top_10_betw2 <- tail(sort(betw2), 10)
top_10_betw2
   Auckland District Health Board           Plant and Food Research                    AUT University 
                         48988.50                          57655.33                          74583.33 
            University of Waikato                        AgResearch Victoria University of Wellington 
                         81434.50                          96575.50                         139495.17 
         University of Canterbury                 Massey University               University of Otago 
                        198521.67                         323919.17                         340995.17 
           University of Auckland 
                        815924.25 
bottom_10_betw2 <- head(sort(betw2), 10)
bottom_10_betw2
                45 South Management Ltd.                               Abacus ALS 
                                       0                                        0 
                       ABB Power Quality      ABI Rehabilitation New Zealand Ltd. 
                                       0                                        0 
                  AC Research Associates      Academic Colleges Group New Zealand 
                                       0                                        0 
       Accident Compensation Corporation Action on Smoking and Health New Zealand 
                                       0                                        0 
                           Active Health                Acurity Health Group ltd. 
                                       0                                        0 
betw2["University of Auckland"]
University of Auckland 
              815924.2 

Вывод: При разных методах минимальные значения центральности у вершин будут равны 0. Это вершины, расположенные на периферии графа, или те, которые вовсе имеют всего одного соседа (например, та 21 пара вершин). Максимальные центральности вершин превышают 40 000 в топ-10. В обоих случаях университет Окленда на первом месте (3.8542147^{5} и 8.1592425^{5}). Значительное число кратчайших путей между любыми двумя вершинами проходит именно через данный университет.

Центральность по собственному значению

eig1 <- eigen_centrality(net, weights = NA)
head(eig1)
$vector
                                       45 South Management Ltd. 
                                                   0.0085447751 
                                                     Abacus ALS 
                                                   0.0225025837 
                                                 AbacusBio Ltd. 
                                                   0.0634333214 
                                              ABB Power Quality 
                                                   0.0148191986 
                            ABI Rehabilitation New Zealand Ltd. 
                                                   0.0073868398 
                                         AC Research Associates 
                                                   0.0424816145 
                            Academic Colleges Group New Zealand 
                                                   0.0249346566 
                              Accident Compensation Corporation 
                                                   0.1565499955 
                       Action on Smoking and Health New Zealand 
                                                   0.0249346566 
                                                  Active Health 
                                                   0.0221603845 
                                      Acurity Health Group ltd. 
                                                   0.1302323254 
                                                Ade Consultants 
                                                   0.0249346566 
                                         Adidas Sports Medicine 
                                                   0.0249346566 
                                        Adis International Ltd. 
                                                   0.0336599761 
                                Advanced Clinical Skills Centre 
                                                   0.0357429619 
                                                          AECOM 
                                                   0.0509845147 
                                                      AECS Ltd. 
                                                   0.0109051918 
                                                  Aerocool Ltd. 
                                                   0.0109051918 
                                                  Aeroqual Ltd. 
                                                   0.0577525103 
                                              Affinity Services 
                                                   0.0249346566 
                                        AFT Pharmaceuticals Ltd 
                                                   0.0587637808 
                                             AFTpharmaceuticals 
                                                   0.0249346566 
                                  Agencies for Nutrition Action 
                                                   0.0217906430 
                                Agile Utilities New Zealand Ltd 
                                                   0.0169041147 
                                               Agknowledge Ltd. 
                                                   0.0212009962 
                                                     AgResearch 
                                                   0.3760716410 
                                             Agri-Optic NZ Ltd. 
                                                   0.0169041147 
                                             Agribusiness Group 
                                                   0.0295790148 
                                    AgriGenesis Biosciences Ltd 
                                                   0.0248896704 
                                          AgriHealth NZ Limited 
                                                   0.0017355927 
                                        Agrimm Technologies Ltd 
                                                   0.0085515239 
                                                AgriNova NZ Ltd 
                                                   0.0089944603 
                                            AgriQuality Limited 
                                                   0.0083317141 
                                         Agvance Marketing Ltd. 
                                                   0.0262813319 
                                                Air New Zealand 
                                                   0.0915449278 
                                               Air Quality Ltd. 
                                                   0.0263746957 
                                            Airborne Honey Ltd. 
                                                   0.0172367328 
                                          Akaroa Medical Centre 
                                                   0.0212473008 
  Ako Aotearoa National Centre for Tertiary Teaching Excellence 
                                                   0.0145768290 
                              Akoranga Integrated Health Clinic 
                                                   0.0117204425 
                                       Alan Bell and Associates 
                                                   0.0125723173 
                       Albany Basin Accident and Medical Centre 
                                                   0.0073486957 
                        Alcohol Advisory Council of New Zealand 
                                                   0.0032664850 
                       Alcohol Harm Minimisation Advisory Group 
                                                   0.0340265148 
                                      Alcohol Healthwatch Trust 
                                                   0.0249346566 
                                           Alexandra Lions Club 
                                                   0.0091827677 
                                       Alexandra Medical Centre 
                                                   0.0212473008 
                                              Alfriston College 
                                                   0.0109051918 
                                           All Seasons Pharmacy 
                                                   0.0249346566 
                               Allan Planning and Research Ltd. 
                                                   0.0090730520 
      Allen & Clarke  Policy and Regulatory Specialists Limited 
                                                   0.0555077759 
                                                      Alphalabs 
                                                   0.0187458603 
                         Alpine and Polar Processes Consultancy 
                                                   0.0376639866 
                                           Alzheimers Northland 
                                                   0.0000000000 
                        Amalgamates Solutions and Research Ltd. 
                                                   0.0191731508 
                                            Amity Health Centre 
                                                   0.0212473008 
                                        Ancare New Zealand Ltd. 
                                                   0.0212473008 
                                          Ancare Scientific Ltd 
                                                   0.0478431997 
                                                      Anexa FVC 
                                                   0.0696056383 
                                Anglesea Medical Properties Ltd 
                                                   0.0548045432 
                                          Animal Dermatology NZ 
                                                   0.0121559609 
                                Animal Health Board New Zealand 
                                                   0.0279399293 
         Animals and Marine Surveillance and Investigation Team 
                                                   0.0169041147 
                                     Animation Research Limited 
                                                   0.0212473008 
                                       Antarctic Heritage Trust 
                                                   0.0109051918 
                                         Antarctica New Zelaand 
                                                   0.0663104085 
                                  Antarctica Scientific Limited 
                                                   0.0168318809 
                                     Antipodean Pharmaceuticals 
                                                   0.0429201429 
                                    Aorangi Veterinary Services 
                                                   0.0024756390 
                                           Aotea Pathology Ltd. 
                                                   0.1298345651 
               Aotearoa Alcohol and Other Drug Consumer Network 
                                                   0.0473629359 
                                                AP EnerTec Ltd. 
                                                   0.0000000000 
                              Applied Engineering Research Ltd. 
                                                   0.0069284140 
                         Applied Research and Technologies Ltd. 
                                                   0.0096102637 
                        Applied Research Associates New Zealand 
                                                   0.0091965786 
                                       AquaBio Consultants Ltd. 
                                                   0.0164247640 
                                        Aquaculture New Zealand 
                                                   0.0444266381 
                                         Aqualinc Research Ltd. 
                                                   0.1105440131 
                                        Aquanet Consulting Ltd. 
                                                   0.0169041147 
                                Aquatic Research Solutions Ltd. 
                                                   0.0325932246 
                                             Aranui High School 
                                                   0.0100397160 
                                                  ARANZ Geo Ltd 
                                                   0.0091965786 
                                         ARANZ Medical Scanning 
                                                   0.0163238496 
                                                 Areograph Ltd. 
                                                   0.0360664993 
                                               ARH Construction 
                                                   0.0249346566 
                                                Aroa Biosurgery 
                                                   0.1021961716 
                                               Arohanui Hospice 
                                                   0.0055984690 
                                        Arotec Diagnostics Ltd. 
                                                   0.0253678019 
                                              Ascot Angiography 
                                                   0.0295960666 
                     Ascot Women's Cancer Centre of New Zealand 
                                                   0.0021854512 
                                    Asia New Zealand Foundation 
                                                   0.0504330082 
                                       Asphalt Products Limited 
                                                   0.0148191986 
                                Aspiring Veterinary Service Ltd 
                                                   0.0184484581 
                    ASR Limited Martine Consulting and Research 
                                                   0.0325771915 
                                     Assa Abloy New Zealand Ltd 
                                                   0.0212473008 
                                      Assistive Technology Ltd. 
                                                   0.0169041147 
                                        Assurity Consulting Ltd 
                                                   0.0117204425 
                                                   AsureQuality 
                                                   0.0336871569 
                                              AsureQuality Ltd. 
                                                   0.0650833395 
                                                    At the Vets 
                                                   0.0193797536 
                                 Atkinson and Rapley Consulting 
                                                   0.0169041147 
                                            Atlantis HealthCare 
                                                   0.0249346566 
                         Auckland-Waikato Fish and Game Council 
                                                   0.0145768290 
                                  Auckland Astronomical Society 
                                                   0.0381483638 
                                       Auckland Botanic Gardens 
                                                   0.0387406275 
                                         Auckland Breast Centre 
                                                   0.0073486957 
                                          Auckland City Mission 
                                                   0.0644644056 
                                 Auckland Clinical Studies Ltd. 
                                                   0.0462106883 
                                               Auckland Council 
                                                   0.2514405100 
                                      Auckland Cricket Assn Inc 
                                                   0.0117204425 
                                           Auckland Dermatology 
                                                   0.0073868398 
                                 Auckland District Health Board 
                                                   0.4334651746 
                                                   Auckland Eye 
                                                   0.0456739513 
                                           Auckland Heart Group 
                                                   0.0543955521 
                                  Auckland Institute of Studies 
                                                   0.0151004270 
                         Auckland International Airport Limited 
                                                   0.0117204425 
                                                Auckland Museum 
                                                   0.1651970874 
                           Auckland Refugee Community Coalition 
                                                   0.0249346566 
                                      Auckland Regional Council 
                                                   0.0249346566 
                         Auckland Southern Cross Hospital Group 
                                                   0.0322833524 
                                             Auckland Transport 
                                                   0.0249346566 
                                                   Auckland Zoo 
                                                   0.1238622030 
                                                        Aurecon 
                                                   0.0621103982 
            Australian and New Zealand College of Anaesthetists 
                                                   0.0357429619 
                                                 AUT University 
                                                   0.4700462773 
                                          Automation Design Ltd 
                                                   0.0025280601 
               Aviation Industry Association of New Zealand Inc 
                                                   0.0000000000 
                                                     Avivet Ltd 
                                                   0.0262813319 
                                       Avocado Industry Council 
                                                   0.0083317141 
                                        Babbage Consulting Ltd. 
                                                   0.0556394773 
                                Ballance Agri-Nutrients Limited 
                                                   0.0841401665 
                                               Bank of Scotland 
                                                   0.0249346566 
                                              Bartonk Solutions 
                                                   0.0108361949 
                                 Batten Animal Research Network 
                                                   0.0297988246 
                                      Baxter Healthcare Limited 
                                                   0.0778439353 
                                                  Bay Audiology 
                                                   0.0148191986 
                            Bay of Plenty District Health Board 
                                                   0.2006176989 
                                      Bay of Plenty Polytechnic 
                                                   0.1214434910 
                                 Bay of Plenty Regional Council 
                                                   0.0498932908 
                                                    Bay Urology 
                                                   0.0188880385 
                                  Bayer CropScience New Zealand 
                                                   0.0096082207 
                                      Bayleys Property Services 
                                                   0.0249346566 
                                             BC Consulting Ltd. 
                                                   0.0105686304 
                                            BCRL Energy Limited 
                                                   0.0015532672 
                                                           Beca 
                                                   0.1085507044 
                                      Beef and Lamb New Zealand 
                                                   0.0653301154 
                                             Bennett Scientific 
                                                   0.0600119714 
                                           Benthic Science Ltd. 
                                                   0.0303203528 
                                                 Berryworld Ltd 
                                                   0.0171016191 
                                  Best Practice Advocacy Centre 
                                                   0.0461819574 
                                                 Beta Solutions 
                                                   0.0418387713 
                                                  Bethesda Care 
                                                   0.0322833524 
                                        Betta Bees Research Ltd 
                                                   0.0212473008 
                                      Better Border Biosecurity 
                                                   0.0175144817 
                                      BHU Future Farming Centre 
                                                   0.0233707224 
                                       Bickler Consultants Ltd. 
                                                   0.0570871492 
                                                         BikeNZ 
                                                   0.0148191986 
                                          Bio Soil and Crop Ltd 
                                                   0.0000000000 
                                Bioactives Research New Zealand 
                                                   0.0647089028 
                                  Biodiscovery New Zealand Ltd. 
                                                   0.0625963784 
                                                 Biomarine Ltd. 
                                                   0.0249346566 
                                                Biomatters Ltd. 
                                                   0.0461819574 
                                         Biometrics Matters Ltd 
                                                   0.0561137714 
                                         Biopolymer Network Ltd 
                                                   0.0662200775 
                                        Biosecurity New Zealand 
                                                   0.0334589485 
                                BioSylve Forest Science NZ Ltd. 
                                                   0.0069284140 
                              BirdLife Global Seabird Programme 
                                                   0.0088708385 
                                               Blind Foundation 
                                                   0.0169041147 
                                         BLIS Technologies Ltd. 
                                                   0.0453709988 
                                     Blue Water Marine Research 
                                                   0.0340077087 
                                               Blues Rugby Club 
                                                   0.0000000000 
                                             Bodeker Scientific 
                                                   0.0599799055 
                                            Body Aid Clinic Ltd 
                                                   0.0212473008 
                                              Boffa Miskell Ltd 
                                                   0.1279181462 
                                         Bomac Laboratories Ltd 
                                                   0.0516696117 
                                              Boulcott Hospital 
                                                   0.0050021543 
                                               Braemar Hospital 
                                                   0.0344357356 
                                                     BRANZ Ltd. 
                                                   0.1304195764 
                                       Bream Bay Medical Centre 
                                                   0.0249346566 
                             Breast Care and Screening Services 
                                                   0.0323214964 
                        Breast Surgeons' Society of New Zealand 
                                                   0.0249346566 
                                               Breen Consulting 
                                                   0.0181546078 
                   Brian Ricketts Geological Consulting Limited 
                                                   0.0077405813 
                                        Broadway Medical Centre 
                                                   0.0330143899 
                                       Broadway Surgical Clinic 
                                                   0.0136782023 
                                           Broken Hills Gold Co 
                                                   0.0249346566 
                                          Brownrigg Agriculture 
                                                   0.0068977582 
                                  Bruce Shallard and Associates 
                                                   0.0000000000 
                                             Bunnythorpe School 
                                                   0.0091827677 
                                   Cadwallader Tree Consultancy 
                                                   0.0148191986 
                                         Cahill Animal Hospital 
                                                   0.0169041147 
                                     CAL Engineering Management 
                                                   0.0153758990 
                                           Callaghan Innovation 
                                                   0.2234003482 
                                               Cambridge Clinic 
                                                   0.0339592927 
                                  Cambridge Veterinary Services 
                                                   0.0121559609 
                                         Cameron Medical Clinic 
                                                   0.0472233491 
                                   Campbell and Associates Ltd. 
                                                   0.0083317141 
                          Cancer Control Council of New Zealand 
                                                   0.0478920383 
                                  Cancer Society of New Zealand 
                                                   0.0860232744 
                              Canterbury Charity Hospital Trust 
                                                   0.0372006247 
        Canterbury Civil Defence and Emergency Management Group 
                                                   0.0119788176 
                               Canterbury District Health Board 
                                                   0.4357203327 
                       Canterbury Earthquake Recovery Authority 
                                                   0.0442329677 
                                          Canterbury Health Ltd 
                                                   0.0792525326 
                                     Canterbury Medical Imaging 
                                                   0.0278119441 
                                              Canterbury Museum 
                                                   0.1900636996 
                  Canterbury Rugby Football Union and Crusaders 
                                                   0.0129927456 
                                      CanZealand Geoscience Ltd 
                                                   0.0082679590 
              Cape Kidnappers and Ocean Beach Wildlife Preserve 
                                                   0.0255722930 
                                                 Cape Sanctuary 
                                                   0.0376177111 
                        Capital and Coast District Health Board 
                                                   0.3177595138 
                                        Capital Eye Specialists 
                                                   0.0121523837 
                                               Capital Research 
                                                   0.0291705251 
                                             Carbon Partnership 
                                                   0.0091827677 
                                Cardiac Inherited Disease Group 
                                                   0.0357429619 
                                    Care of Orca Research Trust 
                                                   0.0004217605 
                                          Carey Baptist College 
                                                   0.0249346566 
                                         Carroll Consulting ltd 
                                                   0.0224745256 
                                         Carson Associates Ltd. 
                                                   0.0069284140 
                                        Carter Holt Harvey Ltd. 
                                                   0.0545001079 
                                    Carter National Observatory 
                                                   0.0326965585 
                                                Cashmere Health 
                                                   0.0217906430 
                                                     Catch Ltd. 
                                                   0.0249346566 
                                                         Catmed 
                                                   0.0071244369 
                                             Cawthron Institute 
                                                   0.2826406171 
                                    CBG Health Research Limited 
                                                   0.0741632077 
                                              Centennial Health 
                                                   0.0223625034 
                               Center for Backyard Astrophysics 
                                                   0.0046759434 
          Central and Southern New Zealand Craniofacial Program 
                                                   0.0430994673 
                                              Central City Vets 
                                                   0.0173363916 
                                          Central Otago Tourism 
                                                   0.0212473008 
                                         Central Stories Museum 
                                                   0.0091827677 
                                                     CentralMed 
                                                   0.0774218017 
                               Centre for Backyard Astrophysics 
                                                   0.0948879961 
            Centre for Clinical Research and Effective Practice 
                                                   0.0742382356 
                                    Centre for Dairy Excellence 
                                                   0.0173363916 
              Centre for Minerals Environmental Research (CMER) 
                                                   0.0228005680 
           Centre for Research Evaluation and Social Assessment 
                                                   0.0033351276 
                      Centre for Youth Health in South Auckland 
                                                   0.0330143899 
                                              CH and Associates 
                                                   0.0310106277 
                                     ChangeMakers Refugee Forum 
                                                   0.0000000000 
                                    Chatham Rock Phosphate Ltd. 
                                                   0.0000000000 
                                              Chemipreneur Ltd. 
                                                   0.0384093576 
                                       Chemistry Communications 
                                                   0.0322833524 
                                   Chiefs Super Rugby Franchise 
                                                   0.0222977389 
                                         Child and Youth Health 
                                                   0.0371987277 
                                     Child Poverty Action Group 
                                                   0.0249346566 
                                     Chilton Saint James School 
                                                   0.0000000000 
                                                   Chiptech Ltd 
                                                   0.0217906430 
                                      Christchurch City Council 
                                                   0.1258794787 
                         Christchurch Emergency Care Foundation 
                                                   0.0739506089 
               Christchurch Polytechnic Institute of Technology 
                                                   0.1781144112 
                             Christchurch Psychologists' Office 
                                                   0.0360664993 
                                    Christchurch Vascular Group 
                                                   0.0497172699 
                                                  City Care Ltd 
                                                   0.0148191986 
                                                   City Fitness 
                                                   0.0460746398 
                                       Civil Aviation Authority 
                                                   0.0418387713 
                                                          Claro 
                                                   0.0249346566 
                                     ClearSight Consultants Ltd 
                                                   0.0572131979 
                                     Clement and Associates Ltd 
                                                   0.0154066930 
                    Clendon Burns and Park Consulting Engineers 
                                                   0.0111340106 
                                               CLIMsystems Ltd. 
                                                   0.0109051918 
                                              Clinical Horizons 
                                                   0.0311176247 
                                               Clinical Systems 
                                                   0.0080797332 
                                  Clutha Veterinary Association 
                                                   0.0237229397 
                                        Coast and Catchment Ltd 
                                                   0.0465901427 
                                   Coast to Coast Health Centre 
                                                   0.0073486957 
                                Coastal and Aquatic Systems Ltd 
                                                   0.0537592324 
                                      Coastal Systems (NZ) Ltd. 
                                                   0.0031067036 
                                          Coastline Consultants 
                                                   0.0069284140 
                                    Cognition Education Limited 
                                                   0.0249346566 
                                                       Cognosco 
                                                   0.0395351994 
                                          Colgate-Palmolive Ltd 
                                                   0.0148191986 
                                           Colin Christian Ltd. 
                                                   0.0212473008 
                                          Collins Carriers Ltd. 
                                                   0.0085515239 
                                                 Colmar Brunton 
                                                   0.0249346566 
                                                Columba College 
                                                   0.0212473008 
                                              Common Ground Ltd 
                                                   0.0356766685 
                                       Commtest Instruments Ltd 
                                                   0.0148191986 
           Community Clinic for Sexual Health and Contraception 
                                                   0.0249346566 
                                  Compac Sorting Equipment Ltd. 
                                                   0.0332663707 
                                            Compac Technologies 
                                                   0.0169041147 
                                                 Compass Health 
                                                   0.0358004066 
                                  Compusoft Engineering Limited 
                                                   0.0249346566 
                                     Compusoft Engineering Ltd. 
                                                   0.0255722930 
                                             Comtel System Ltd. 
                                                   0.0180783636 
                                       Comvita New Zealand Ltd. 
                                                   0.0576211479 
                                           Connectos Consulting 
                                                   0.0385790078 
                                               Connovation Ltd. 
                                                   0.0804404351 
                      Conservation and Environmental Management 
                                                   0.0164100305 
                                   Construction Techniques Ltd. 
                                                   0.0397538552 
                                     Consulting Dietitians Ltd. 
                                                   0.0357429619 
                                            Contact Energy Ltd. 
                                                   0.0372421227 
                                        Contract Landscapes Ltd 
                                                   0.0031067036 
                                            CORE Education Ltd. 
                                                   0.0358398484 
                                                       Cosgrove 
                                                   0.0148191986 
                         Counties Manukau District Health Board 
                                                   0.3240362737 
                                                      Covec Ltd 
                                                   0.0547334813 
                                           CPG New Zealand Ltd. 
                                                   0.0169041147 
                                        Crawford Medical Centre 
                                                   0.0255722930 
                                                CRL Energy Ltd. 
                                                   0.0622935069 
                                               Cromwell College 
                                                   0.0145768290 
                                         Cropmark Seeds Limited 
                                                   0.0275757006 
                                   Crown Fibre Holdings Limited 
                                                   0.0000000000 
                                CURT St George's Medical Centre 
                                                   0.0717204409 
                                       Cuttriss Consultants Ltd 
                                                   0.0082679590 
                                        Cymbiotix Group Limited 
                                                   0.0366550992 
                                                    Cyperus Ltd 
                                                   0.0610011560 
                                         Dairy Consultants Ltd. 
                                                   0.0032528812 
                              Dairy Goat Co-operative (NZ) Ltd. 
                                                   0.0608505861 
                                  Dairy Production Systems Ltd. 
                                                   0.0002339632 
                                                        DairyNZ 
                                                   0.1976925650 
                                    David Butler Associates Ltd 
                                                   0.0169041147 
                                    Davidson Environmental Ltd. 
                                                   0.0608123459 
                                                 DaVinci Clinic 
                                                   0.0009407940 
                                       DCM Process Control Ltd. 
                                                   0.0249346566 
                             DEA Research Software Surgery Ltd. 
                                                   0.0249346566 
                                            Deepwater Group Ltd 
                                                   0.0154066930 
                                                         DeerNZ 
                                                   0.0083317141 
                                                       Deloitte 
                                                   0.0779052706 
                                     Department of Conservation 
                                                   0.3434545723 
                                      Department of Corrections 
                                                   0.0148191986 
                                             Development Action 
                                                   0.0145768290 
                                          Development By Design 
                                                   0.0145768290 
                                           Devon Medical Centre 
                                                   0.0058923147 
                                      DHI Water and Environment 
                                                   0.0031407143 
                                             Diabetes Otago Inc 
                                                   0.0212473008 
                                          Diagnostic Laboratory 
                                                   0.0438226952 
                                              Diagnostic Medlab 
                                                   0.1020326684 
                                      Digestive Health Services 
                                                   0.0321118376 
                                        Digital Sensing Limited 
                                                   0.0395114857 
                                             Disability Connect 
                                                   0.0255722930 
                                     Disability Resource Centre 
                                                   0.0385790078 
                                                   Diversity NZ 
                                                   0.0385790078 
                                                 DM Consultants 
                                                   0.0534911546 
                                           DNA Investments Ltd. 
                                                   0.0067545733 
                          Dnature diagnostics and research Ltd. 
                                                   0.0643217854 
                                  Doctors for Sexual Abuse Care 
                                                   0.0256275039 
                                            Donaghys Industries 
                                                   0.0085447751 
                                       Donald Beasley Institute 
                                                   0.0675474430 
                                    Dorothy-Jean and Associates 
                                                   0.0093686431 
                                                  Dovedale Ltd. 
                                                   0.0630860720 
                                       Downer EDI Works Limited 
                                                   0.0145215529 
                                      Dr. Malcolm McKellar Ltd. 
                                                   0.0028159529 
                                                 Dragonfly Ltd. 
                                                   0.0643386817 
                            Drummond Food Science Advisory Ltd. 
                                                   0.0212473008 
                                           Dumpark Data Science 
                                                   0.0003351217 
                                               Duncan Cotterill 
                                                   0.0227419482 
                                           Dunedin City Council 
                                                   0.0250801257 
                                     Dunedin Heat Pumps Limited 
                                                   0.0212473008 
                                Dunedin South Veterinary Clinic 
                                                   0.0169041147 
                              Dunning Thornton Consultants Ltd. 
                                                   0.0280413602 
                                          Dynamic Controls Ltd. 
                                                   0.0301367406 
                                                       Dynatest 
                                                   0.0292907106 
                         Dyspraxia Support Group of New Zealand 
                                                   0.0321118376 
                                          Earthquake Commission 
                                                   0.0608212113 
                                   Earthtech Consulting Limited 
                                                   0.0255722930 
                                Eastern Institute of Technology 
                                                   0.1355536810 
                                   Eastern Region Fish and Game 
                                                   0.0212223159 
              Eastern Suburbs Association Football Club (ESAFC) 
                                                   0.0418387713 
                              Eastland Veterinary Services Ltd. 
                                                   0.0193797536 
                                       Eaton Power Quality Ltd. 
                                                   0.0148191986 
                                                ECG Consultants 
                                                   0.0169041147 
                        Eco-Vista Photography and Research Ltd. 
                                                   0.0834663789 
                                                 Eco Nomos Ltd. 
                                                   0.0184502693 
                                    Eco Research Associates Ltd 
                                                   0.0783329188 
                                                 ECoast Limited 
                                                   0.0134399958 
                                      EcoGecko Consultants Ltd. 
                                                   0.0535708193 
                                     Ecosynergy Group Ltd (EGL) 
                                                   0.0145768290 
                                                      Ectus Ltd 
                                                   0.0109051918 
                           Edmund Lawler and Associates Limited 
                                                   0.0145768290 
                                                Education House 
                                                   0.0000000000 
                                        Education Review Office 
                                                   0.0249346566 
                                 Educational Leadership Project 
                                                   0.0109051918 
                                          Electricity Authority 
                                                   0.0543306842 
                    Eli Lilly and Company (New Zealand) Limited 
                                                   0.0322162022 
                                           Elmwood Orthopaedics 
                                                   0.0222124035 
                            Eltham District Veterinary Services 
                                                   0.0351889468 
                                             Endoscopy Auckland 
                                                   0.0281588178 
                   Energy Efficiency and Conservation Authority 
                                                   0.0570927062 
                                 Energy Solution Providers Ltd. 
                                                   0.0085515239 
                                                    EnForm Tech 
                                                   0.0154523504 
                                         Enigma Publishing Ltd. 
                                                   0.0357633071 
                                                      Ensys Ltd 
                                                   0.0148191986 
                                                   Entecol Ltd. 
                                                   0.0655898892 
                                     Enviro-Mark Solutions Ltd. 
                                                   0.0148191986 
                                                Enviro Research 
                                                   0.0096170142 
                                         Environment Canterbury 
                                                   0.1589865237 
                          Environment Protection Authority(EPA) 
                                                   0.0392141743 
                              Environmental Management Services 
                                                   0.0082679590 
                                  Environmental Restoration Ltd 
                                                   0.0069284140 
                                    ENZO Nutraceuticals Limited 
                                                   0.0337630125 
                                                Epi-interactive 
                                                   0.0598731008 
                                     Epsom Girls Grammar School 
                                                   0.0249346566 
                                      Equine Health Association 
                                                   0.0067545733 
                                                    ERA Ecology 
                                                   0.0621586728 
                                                      Erin Park 
                                                   0.0424816145 
                                                            ESR 
                                                   0.3757277751 
                                            Etec Crop Solutions 
                                                   0.0083317141 
                                     Eudyptes EcoConsulting Ltd 
                                                   0.0298112226 
                                                     Explore NZ 
                                                   0.0169041147 
                                                  Eye Institute 
                                                   0.0357429619 
                                     Far North District Council 
                                                   0.0197207777 
                                          Farm Cove Observatory 
                                                   0.0926398885 
                                        Feilding Medical Centre 
                                                   0.0379873515 
                                                       FEM Ltd. 
                                                   0.0000000000 
                                       Fern Research Foundation 
                                                   0.0202866077 
                                                Ferndale School 
                                                   0.0148191986 
                                           Fertility Associates 
                                                   0.0819656056 
                                    Financial Markets Authority 
                                                   0.0145768290 
                                               Fish and Game NZ 
                                                   0.0310106277 
                                   Fisher and Paykel Appliances 
                                                   0.0249346566 
                              Fisher and Paykel Healthcare Ltd. 
                                                   0.1224453025 
                        Fishing Vessel Management Services Ltd. 
                                                   0.0203179504 
                                            FitzRoy of Merivale 
                                                   0.0240019662 
                                       Fletcher Construction Co 
                                                   0.0270640959 
                                                  FMR GROUP LTD 
                                                   0.0101758024 
                                                       Fonterra 
                                                   0.2380157231 
                              Food and Bio-based Products Group 
                                                   0.0346130460 
                                          Food and Health Group 
                                                   0.0346130460 
                                Foot Science International Ltd. 
                                                   0.0212473008 
                            Forensic and Industrial Science Ltd 
                                                   0.0249346566 
                                                Forest and Bird 
                                                   0.0512985933 
                                             Forever Beech Ltd. 
                                                   0.0148191986 
                                 Foundation for Arable Research 
                                                   0.0369526604 
                 Foundation for Research Science and Technology 
                                                   0.0169041147 
                        Fox and Associates-Consulting Surveyors 
                                                   0.0230871576 
                                        Fred Hollows Foundation 
                                                   0.0536255208 
  Fresenius Medical Care Australia Pty Ltd (New Zealand Branch) 
                                                   0.0330143899 
                                               Freshport NZ Ltd 
                                                   0.0085515239 
                                           Frontier Global Ltd. 
                                                   0.0249346566 
                                              Fruitfed Supplies 
                                                   0.0094809400 
                                          Fruition Horticulture 
                                                   0.0265793209 
                                              FullSpectrum Ltd. 
                                                   0.0109051918 
                                              Fulton Hogan Ltd. 
                                                   0.0501049765 
                                        Future Forests Research 
                                                   0.0069284140 
                                                   Future Steps 
                                                   0.0610011560 
                                            FuturebyDesign Ltd. 
                                                   0.0439934000 
                                                FutureMATH Ltd. 
                                                   0.0015017680 
                            Gallagher Animal Management Systems 
                                                   0.0109051918 
                                              Gambling Helpline 
                                                   0.0286245572 
                 Genesis Research & Development Corporation Ltd 
                                                   0.0461819574 
                                      Genetic Technologies Ltd. 
                                                   0.0169041147 
                                               Gentrack Limited 
                                                   0.0160004160 
                                       Geoenvironmetal Services 
                                                   0.0025725030 
                                                         GEOKEM 
                                                   0.0262567192 
                                             Geomarine Research 
                                                   0.1307263209 
                                      Geoscience Consulting Ltd 
                                                   0.0249346566 
                                         Geotech Consulting Ltd 
                                                   0.0239085786 
                                     Geothermal Engineering Ltd 
                                                   0.0249346566 
                                            Geoventures Limited 
                                                   0.0212473008 
                                    GF McLaren Research Limited 
                                                   0.0085447751 
                                    GHD Centre Level Napier St. 
                                                   0.0249346566 
                                                    GHD Limited 
                                                   0.0000000000 
                             Gillies McIndoe Research Institute 
                                                   0.0911656099 
                                      Gisborne District Council 
                                                   0.0111340106 
                                           Glass Earth Gold Ltd 
                                                   0.0212473008 
                                        Glenview Medical Centre 
                                                   0.0332561553 
           Global Action for Health Equity Network (HealthGAEN) 
                                                   0.0169041147 
                               Global Public Health Company Ltd 
                                                   0.0673236461 
                                                    GNS Science 
                                                   0.3315850368 
                                              Golden Bay Cement 
                                                   0.0255722930 
                                     Golder Associates (NZ) Ltd 
                                                   0.1044139017 
                                Good Life Research Centre Trust 
                                                   0.0151073910 
                                                         Google 
                                                   0.0145768290 
                            Greater Wellington Regional Council 
                                                   0.0728700020 
                                            Green Lane Hospital 
                                                   0.0073486957 
                                   Greenweaver Architecture Ltd 
                                                   0.0178287964 
                                Greerton Early Childhood Centre 
                                                   0.0257243904 
                                            Gribbles Veterinary 
                                                   0.0992850638 
                                                   GroPlus Ltd. 
                                                   0.0000000000 
                                       Ground Investigation Ltd 
                                                   0.0249346566 
                                               Growth Solutionz 
                                                   0.0000000000 
                                    Guardian Health Care (Bupa) 
                                                   0.0424816145 
                                       Hagley Community College 
                                                   0.0148191986 
                                                   Hally Labels 
                                                   0.0145768290 
                                            Hamilton Eye Clinic 
                                                   0.0249346566 
                        Hamilton Sacred Heart College for Girls 
                                                   0.0109051918 
                                   Hamilton Veterinary Services 
                                                   0.0169041147 
                                                   Hamilton Zoo 
                                                   0.0927657568 
                                             Hanham Consultants 
                                                   0.0249346566 
                                         Hanmer Clinic Tauranga 
                                                   0.0212473008 
                                      Hapai Te Hauora Tapui Ltd 
                                                   0.0366550992 
                        Harker Underground Construction Limited 
                                                   0.0151981595 
                                              Harris Consulting 
                                                   0.0209783294 
                                              Hauora Heretaunga 
                                                   0.0249346566 
                                           Hauora Waikato Group 
                                                   0.0492256111 
                                      Hauraki Maori Trust Board 
                                                   0.0411532437 
                           Hawke's Bay Alcohol and Drug Service 
                                                   0.0416621294 
                              Hawke's Bay District Health Board 
                                                   0.2058971165 
                                   Hawke's Bay Regional Council 
                                                   0.0911863123 
                                                  Hawkins Watts 
                                                   0.0249346566 
                                                Health Alliance 
                                                   0.0309912817 
                                           Health Care Aotearoa 
                                                   0.0148191986 
                                        Health New Zealand Ltd. 
                                                   0.1496627014 
                                Health Outcomes Associates Ltd. 
                                                   0.0249346566 
                               Health Partners Consulting Group 
                                                   0.0874820562 
                                        Health Promotion Agency 
                                                   0.1078352175 
                           Health Quality and Safety Commission 
                                                   0.0785713611 
                                       Healthscope Laboratories 
                                                   0.0041860189 
                                                     HealthWEST 
                                                   0.0571097128 
                                Heart Foundation of New Zealand 
                                                   0.0470104811 
                         Heavy Engineering Research Association 
                                                   0.0616612301 
                                               HEB Construction 
                                                   0.0015883053 
                                                 Heinz Wattie's 
                                                   0.0257653650 
                                                Heke Consulting 
                                                   0.0249346566 
                              Helios Integrative Medical Centre 
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                                                       Hemptech 
                                                   0.0109051918 
                                       Henderson Medical Centre 
                                                   0.0595109013 
                                Henderson Valley Primary School 
                                                   0.0109051918 
                            Hepatitis Foundation of New Zealand 
                                                   0.0961128542 
                                     Herbert Morton Accountants 
                                                   0.0109051918 
                                              Heretaunga Health 
                                                   0.0357429619 
                            Heritage New Zealand Pouhere Taonga 
                                                   0.0249346566 
                             High Performance Sport New Zealand 
                                                   0.0421276382 
                                        Highnam Associates Ltd. 
                                                   0.0249346566 
                                         Hill Laboratories Ltd. 
                                                   0.0754071544 
                                             Hiway Geotechnical 
                                                   0.0249346566 
                     HodderBalog Social and Scientific Research 
                                                   0.0145768290 
                                                    Holcim (NZ) 
                                                   0.0000000000 
                                        Holmes Consulting Group 
                                                   0.0765103830 
                                         Holmes Fire and Safety 
                                                   0.0408654475 
                                      Horizons Regional Council 
                                                   0.1036948576 
                                  Horowhenua Community Practice 
                                                   0.0212473008 
                                       Horowhenua Library Trust 
                                                   0.0000000000 
                                                    Horteye Ltd 
                                                   0.0087581371 
                                                       HortPlus 
                                                   0.0117560195 
                                            Hospice New Zealand 
                                                   0.0728864487 
                              Hospice Palliative Care Education 
                                                   0.0484356873 
                                                Hospice Waikato 
                                                   0.0374843300 
                                             Hot Solutions Ltd. 
                                                   0.0341312352 
                                         Humes Pipeline Systems 
                                                   0.0249346566 
                                          Huntly Community Link 
                                                   0.0000000000 
                                               Hurricanes Rugby 
                                                   0.0200521566 
                                             Hush Interiors Ltd 
                                                   0.0148191986 
                              Hutt Valley District Health Board 
                                                   0.2006105161 
                                             Hyland Consultants 
                                                   0.0144031565 
                          Hyland Fatigue Earthquake Engineering 
                                                   0.0399844100 
                                              Hyperbaric Health 
                                                   0.0571303741 
                                                            IAG 
                                                   0.0148191986 
                              Ian Kusabs and Associates Limited 
                                                   0.0199782438 
                           Ian McLean Consultancy Services Ltd. 
                                                   0.0249346566 
                                                  Ichthyo-niche 
                                                   0.0446304212 
                                                      IGENZ Ltd 
                                                   0.0552512303 
                                                            ILR 
                                                   0.0496341794 
                                   Immunisation Advisory Centre 
                                                   0.0357429619 
                               Inclusive Education Action Group 
                                                   0.0255722930 
                               Independent Petroleum Laboratory 
                                                   0.0332663707 
                                       Indufor Asia-Pacific Ltd 
                                                   0.0116772984 
                                                Infoics Limited 
                                                   0.0106608986 
                                            Inform Planning Ltd 
                                                   0.0367563556 
                               Infrastructure Decisions Limited 
                                                   0.0399912723 
                                  Inglewood Veterinary Services 
                                                   0.0218335109 
                                     Injury Prevention Aotearoa 
                                                   0.0474634045 
                                                 Inland Revenue 
                                                   0.0316922747 
                              Innate Immunotherapeutics Limited 
                                                   0.0694477081 
                                            Innate therapeutics 
                                                   0.0194160608 
                                       Inner City Women's Group 
                                                   0.0249346566 
                                                Inner Zest Ltd. 
                                                   0.0249346566 
                                                 INR Online Ltd 
                                                   0.0058923147 
                                       Insect Science Solutions 
                                                   0.0186163317 
                                                   Insights MSD 
                                                   0.0023543578 
                                                 Inspiring Ltd. 
                                                   0.0481689618 
              Institution of Professional Engineers New Zealand 
                                                   0.0265509510 
                    Intellectual Property Office of New Zealand 
                                                   0.0248896704 
                                Intensive Care Flight Paramedic 
                                                   0.0189598211 
                                                   Interactionz 
                                                   0.0109051918 
                                                        InterAg 
                                                   0.0739432749 
               International Animal Welfare Consultants Limited 
                                                   0.0169041147 
                         International Earth Sciences IESE Ltd. 
                                                   0.0477794447 
                                  International Pacific College 
                                                   0.0169041147 
                International Student Ministries of New Zealand 
                                                   0.0225048305 
                                  International Telematics Ltd. 
                                                   0.0205012141 
                                                      Interpine 
                                                   0.0100114347 
                                         Interpine Forestry Ltd 
                                                   0.0127740846 
                            Intus Digestive and Colorectal Care 
                                                   0.0212473008 
                                             Invenco Group Ltd. 
                                                   0.0249346566 
                                      Investigation Geology Ltd 
                                                   0.0151981595 
                                                          IPENZ 
                                                   0.0384282773 
                                    Irrigation New Zealand Inc. 
                                                   0.0108985458 
                                                       Isolytix 
                                                   0.0212473008 
                                              IZON Science Ltd. 
                                                   0.0905170390 
                                             Jackett Consulting 
                                                   0.0025884288 
                                             Jacobs Engineering 
                                                   0.0270640959 
                                      Jade Software Corporation 
                                                   0.0360664993 
                                               James and Monroe 
                                                   0.0286245572 
                                           JMR Distributors Ltd 
                                                   0.0169041147 
                                               John Jones Steel 
                                                   0.0407710853 
                                           John Wood Consulting 
                                                   0.0409728157 
                                     Johne's Management Limited 
                                                   0.0354640995 
                                         Jowett Consulting Ltd. 
                                                   0.0260880823 
                                                  JRA (NZ) Ltd. 
                                                   0.0249346566 
                             Julian King and Associates Limited 
                                                   0.0181570010 
                                                 Ka Mau Te Wero 
                                                   0.0091827677 
                                        Kaikorai Valley College 
                                                   0.0212473008 
                         Kaikoura Ocean Research Institute Inc. 
                                                   0.0334985785 
                                    Kaipaki Veterinary Services 
                                                   0.0169041147 
                                       Kaipara District Council 
                                                   0.0197207777 
                                  Kapiti Coast District Council 
                                                   0.0208497557 
                                         Karori Sanctuary Trust 
                                                   0.0359299169 
                                                      Katoa Ltd 
                                                   0.0626235739 
                                         Kea Conservation Trust 
                                                   0.0242822369 
                                                 KEA Consultant 
                                                   0.0000000000 
                                                   Keratec Ltd. 
                                                   0.0306245180 
                                      Kidney Health New Zealand 
                                                   0.0828530096 
                             Kina Families and Addictions Trust 
                                                   0.0432853893 
                                     Kinetic Engineering Design 
                                                   0.0249346566 
                                                 Kingdom Clinic 
                                                   0.0258575467 
                                       Kiwi Well Evaluation Ltd 
                                                   0.0358241298 
                                                  Kiwi Wildlife 
                                                   0.0057097786 
                                           Kiwicap Research Ltd 
                                                   0.0000000000 
                      Kiwikiwi Research and Evaluation Services 
                                                   0.0039654969 
                                      Kono Horticulture Limited 
                                                   0.0295790148 
                             Koru Environmental Consultants Ltd 
                                                   0.0161205988 
                                              Koti Technologies 
                                                   0.0148191986 
                                              Kumeu Observatory 
                                                   0.0948345714 
                                           Kurahaupo Consulting 
                                                   0.0091827677 
                                 KVB Kunlun New Zealand Limited 
                                                   0.0169041147 
                                                       Labtests 
                                                   0.0876471356 
                           Lake Hawea Institute of Cryodynamics 
                                                   0.0293960276 
                                    Lakes District Health Board 
                                                   0.1033215235 
                                   Land Information New Zealand 
                                                   0.0560549009 
                                              Landcare Research 
                                                   0.3682732746 
                                       Landcorp Farming Limited 
                                                   0.0514818144 
                                              Langimalie Clinic 
                                                   0.0136242582 
                                              LanzaTech NZ Ltd. 
                                                   0.0281757147 
                              Lassey Research and Education Ltd 
                                                   0.0090730520 
                                             Lateral Technology 
                                                   0.0249346566 
                                          Laura Fergusson Trust 
                                                   0.0321118376 
                                                 Law Commission 
                                                   0.0145768290 
                                       LeaderBrand Produce Ltd. 
                                                   0.0085681181 
                                    Learning for Sustainability 
                                                   0.1117864033 
             Leather & Shoe Research Association of New Zealand 
                                                   0.0310042642 
                                    Leinster Orthopaedic Centre 
                                                   0.0031013897 
                                                 Levare Limited 
                                                   0.0357429619 
                         Levin and Horowhenua Veterinary Centre 
                                                   0.0176209316 
                                          Lewis and Barrow Ltd. 
                                                   0.0153758990 
                                                            LIC 
                                                   0.0958357277 
                                         Life Technologies Ltd. 
                                                   0.0148191986 
                                   LightBox Psychology Services 
                                                   0.0360664993 
                                          Lincoln Agritech Ltd. 
                                                   0.1013874056 
                                             Lincoln University 
                                                   0.3429573541 
                                            Lincolne Scott Ltd. 
                                                   0.0148191986 
                                              Lindis Consulting 
                                                   0.0175531269 
                                            Linnaeus Laboratory 
                                                   0.0125693892 
                                                         Litmus 
                                                   0.0603669014 
                               Livestock Solutions and Services 
                                                   0.0169041147 
                               Living Cell Technologies NZ Ltd. 
                                                   0.0330143899 
                                   Local Government New Zealand 
                                                   0.0305557298 
                                                  Logjiztix Ltd 
                                                   0.0025785973 
                                                        Lowe NZ 
                                                   0.0090730520 
                                     Lucas Industries (NZ) Ltd. 
                                                   0.0249346566 
                                      LWT Animal Nutrition Ltd. 
                                                   0.0173363916 
                              MacMurray Hypertension Clinic Ltd 
                                                   0.0322833524 
                                                          MAGAK 
                                                   0.0077405813 
             Magic Sparks Early Learning and Development Centre 
                                                   0.0438025446 
                                               Magritek Limited 
                                                   0.0395114857 
                                                Makoura College 
                                                   0.0145768290 
                         Malaghan Institute of Medical Research 
                                                   0.1250673199 
                           Male Survivors of Sexual Abuse Trust 
                                                   0.0148191986 
                                              Manaaki Te Awanui 
                                                   0.0579593701 
                      Manaia Health Primary Health Organisation 
                                                   0.0190691382 
                                           Manawatu Diagnostics 
                                                   0.0169041147 
   Mangere Community Health Trust (Primary Health Organisation) 
                                                   0.0556229171 
                                Manukau Institute of Technology 
                                                   0.1442610388 
                                            Manukau SuperClinic 
                                                   0.0249346566 
                                          Manurewa South School 
                                                   0.0249346566 
                                              Maori Hill Clinic 
                                                   0.0212473008 
                                  Maori Pharmacists Association 
                                                   0.0636178473 
                                    Maramatanga Consultants Ltd 
                                                   0.0169041147 
                     Marine Fisheries Research Services Limited 
                                                   0.0065355474 
                                   Marine Wildlife Research Ltd 
                                                   0.0392083571 
                                                Marinoto Clinic 
                                                   0.0346989044 
                          Mark L Batchelar Consulting Engineers 
                                                   0.0148191986 
                                          Market Economics Ltd. 
                                                   0.0169041147 
                               Marlborough Wine Research Center 
                                                   0.0739568360 
                                            MARS Bioimaging Ltd 
                                                   0.0587749017 
                                    Marshall Day Acoustics Ltd. 
                                                   0.0402873112 
                                            Mary Potter Hospice 
                                                   0.0411025740 
                                              Massey University 
                                                   0.6779365323 
                                        Masters Consulting Ltd. 
                                                   0.0065355474 
                                        Matakina Technology Ltd 
                                                   0.0388296394 
                                        Matamata Medical Centre 
                                                   0.0332134020 
                               Matamata Veterinary Services Ltd 
                                                   0.0277859271 
                                                  MBCentury Ltd 
                                                   0.0249346566 
                             McConnell Dowell Constructors Ltd. 
                                                   0.0023284728 
                                          McLaren Research Ltd. 
                                                   0.0083317141 
                                           McManus Geotech Ltd. 
                                                   0.0128106393 
                          Medical Council of New Zealand (MCNZ) 
                                                   0.0025245226 
                      Medical Research Institute of New Zealand 
                                                   0.2167954277 
                                                 Medlab Central 
                                                   0.0900108481 
                                                  Melanoma Unit 
                                                   0.0348275019 
                Member International Neuropsychological Society 
                                                   0.0212473008 
                        Mental Health Education Resource Centre 
                                                   0.0148191986 
                        Mental Health Foundation of New Zealand 
                                                   0.0526470766 
                                           MercyAscot Hospitals 
                                                   0.1293044152 
                                           Meridian Energy Ltd. 
                                                   0.0283020037 
                                                 Mesynthes Ltd. 
                                                   0.0566984213 
                     Meteorological Service of New Zealand Ltd. 
                                                   0.1119667030 
                                                       Methanex 
                                                   0.0185204091 
                                        MetOcean Solutions Ltd. 
                                                   0.0442112677 
                                       Microfossil Research Ltd 
                                                   0.1031697792 
                               MidCentral District Health Board 
                                                   0.2245256123 
                                                    Midland MRI 
                                                   0.0109051918 
                             Midland Regional Forensic Services 
                                                   0.0249346566 
                                        Midlands Health Network 
                                                   0.0357697137 
                               Midwifery Council of New Zealand 
                                                   0.0336253322 
                                        Mighty River Power Ltd. 
                                                   0.0792937180 
                                             Millar Instruments 
                                                   0.0422785094 
                                           Milton Health Centre 
                                                   0.0223625034 
                                Ministry for Primary Industries 
                                                   0.2708909700 
                                  Ministry for Primary Industry 
                                                   0.0448971818 
                                   Ministry for the Environment 
                                                   0.1357076411 
                 Ministry of Business Innovation and Employment 
                                                   0.0983824749 
             Ministry of Civil Defence and Emergency Management 
                                                   0.0145238042 
                                          Ministry of Education 
                                                   0.1290415777 
                          Ministry of Foreign Affairs and Trade 
                                                   0.0415192671 
                                             Ministry of Health 
                                                   0.2428998777 
                                            Ministry of Justice 
                                                   0.0811805803 
                             Ministry of Pacific Island Affairs 
                                                   0.1141955967 
                                 Ministry of Social Development 
                                                   0.0586486465 
                                          Ministry of Transport 
                                                   0.0157957895 
                                 Mission Heights Primary School 
                                                   0.0065355474 
                                       MLB Consulting Engineers 
                                                   0.0148191986 
                              Molehill Astronomical Observatory 
                                                   0.0948345714 
                                       Moorhouse Medical Clinic 
                                                   0.0148218322 
                                       Morrison Consultants Ltd 
                                                   0.0052882317 
                       Motu Economic and Public Policy Research 
                                                   0.1421051798 
                            Mountains to Sea Conservation Trust 
                                                   0.0465901427 
                                          MSD Animal Health Ltd 
                                                   0.0250387059 
                          Mt. Albert Psychological Services Ltd 
                                                   0.0036890855 
                                         Mulgor Consulting Ltd. 
                                                   0.0176761327 
                  Muscular Dystrophy Association of New Zealand 
                                                   0.0856400059 
                                            MWH New Zealand Ltd 
                                                   0.0397538552 
                                             N-Squared Software 
                                                   0.0395114857 
                                          NaeNae Medical Centre 
                                                   0.0150626900 
                                      National Addiction Centre 
                                                   0.0212473008 
               National Association of Steel-Framed Housing Inc 
                                                   0.0264721582 
                       National Council of Women of New Zealand 
                                                   0.0231509127 
                       National Heart Foundation of New Zealand 
                                                   0.1102448403 
  National Library of New Zealand Te Puna Matauranga O Aotearoa 
                                                   0.0227350585 
                   National Maori Health Workforce Organisation 
                                                   0.0212473008 
                                     Natural Resource Assessors 
                                                   0.0455295377 
                                   Needle Exchange Programme NZ 
                                                   0.0473629359 
                                         Nelson Forests Limited 
                                                   0.0217476125 
                       Nelson Marlborough District Health Board 
                                                   0.1696096864 
                               Nelson Marlborough Fish and Game 
                                                   0.0282948475 
                     Nelson Marlborough Institute of Technology 
                                                   0.1441092114 
                            Nelson Marlborough Regional Council 
                                                   0.0356766685 
                                   Neonatal Intensive Care Unit 
                                                   0.0212473008 
                                                        NetSafe 
                                                   0.0249346566 
                                                       NetValue 
                                                   0.0000000000 
                                         Neuren Pharmaceuticals 
                                                   0.0249346566 
                         Neurological Foundation of New Zealand 
                                                   0.0249346566 
                                       New Brighton Health Care 
                                                   0.0327092130 
                                            New Image Group Ltd 
                                                   0.0249346566 
                                                  New River Ltd 
                                                   0.0217906430 
                                   New Zealand Academy of Sport 
                                                   0.1020567927 
                                     New Zealand Aerial Mapping 
                                                   0.0452549932 
        New Zealand Agricultural Greenhouse Gas Research Centre 
                                                   0.0422098659 
                                  New Zealand Agriseeds Limited 
                                                   0.0252358287 
                                    New Zealand AIDS Foundation 
                                                   0.0511842908 
                         New Zealand Aluminium Smelters Limited 
                                                   0.0249346566 
                                New Zealand Antarctic Institute 
                                                   0.0148191986 
                                             New Zealand Arable 
                                                   0.0112508478 
                        New Zealand Association of Optometrists 
                                                   0.0314809437 
                        New Zealand Avocado Growers Association 
                                                   0.0083317141 
           New Zealand BioSecure Entomology Laboratory Research 
                                                   0.0390324680 
                                      New Zealand Blood Service 
                                                   0.1129332944 
                           New Zealand Brain Research Institute 
                                                   0.1117414112 
                           New Zealand Breast Cancer Foundation 
                                                   0.0321118376 
           New Zealand Centre for Conservation Medicine (NZCCM) 
                                                   0.1207957209 
                           New Zealand Climate & Health Council 
                                                   0.0461819574 
                            New Zealand College of Chiropractic 
                                                   0.0366550992 
                                New Zealand College of Midwives 
                                                   0.1309642552 
                              New Zealand Cot Death Association 
                                                   0.0255722930 
           New Zealand Council for Educational Research (NZCER) 
                                                   0.0572053341 
                                      New Zealand Defence Force 
                                                   0.1272999106 
                                 New Zealand Dental Association 
                                                   0.0227419482 
 New Zealand Employment Service and Work and Income New Zealand 
                                                   0.0003697415 
           New Zealand Familial Gastrointestinal Cancer Service 
                                                   0.0615584624 
                                       New Zealand Forestry Ltd 
                                                   0.0072469314 
                    New Zealand Geotechnical Society Ine (NZGS) 
                                                   0.0000000000 
                                   New Zealand Guidelines Group 
                                                   0.0556901454 
                   New Zealand Gynaecological Cancer Foundation 
                                                   0.0342807340 
                  New Zealand Heart and Lung Transplant Service 
                                                   0.0438226952 
             New Zealand Heavy Engineering Research Association 
                                                   0.0445802104 
    New Zealand Homebased Early Childhood Education Association 
                                                   0.0243757323 
         New Zealand Institute for Plastic and Cosmetic Surgery 
                                                   0.0212473008 
                 New Zealand Institute of Community Health Care 
                                                   0.0518148766 
                     New Zealand Institute of Economic Research 
                                                   0.0973370743 
            New Zealand Institute of Medical Laboratory Science 
                                                   0.0336369978 
                          New Zealand Institute of Rural Health 
                                                   0.0461819574 
                                    New Zealand Kiwi Foundation 
                                                   0.0249346566 
                                New Zealand Medical Association 
                                                   0.0332277962 
                      New Zealand Medical Students' Association 
                                                   0.0461819574 
                                  New Zealand National Eye Bank 
                                                   0.0108150294 
                                New Zealand National LCP Office 
                                                   0.0394397671 
                          New Zealand Needle Exchange Programme 
                                                   0.0796199837 
                                New Zealand Nurses Organisation 
                                                   0.0684361320 
                                  New Zealand Olympic Committee 
                                                   0.0212473008 
            New Zealand Organisation for Rare Disorders (NZORD) 
                                                   0.0212473008 
                                         New Zealand Parliament 
                                                   0.0145768290 
                                             New Zealand Police 
                                                   0.0798415549 
                           New Zealand Qualifications Authority 
                                                   0.0145768290 
                                  New Zealand Refining Co. Ltd. 
                                                   0.0148191986 
                           New Zealand Rheumatology Association 
                                                   0.0650699959 
                                        New Zealand Rugby Union 
                                                   0.0587263709 
New Zealand School Acupuncture and Traditional Chinese Medicine 
                                                   0.0148191986 
                                    New Zealand School of Music 
                                                   0.0145768290 
                       New Zealand Seafood Industry Council Ltd 
                                                   0.0207596165 
         New Zealand Society for Earthquake Engineering (NZSEE) 
                                                   0.0000000000 
                                       New Zealand Spinal Trust 
                                                   0.0321118376 
                                   New Zealand Tertiary College 
                                                   0.0366550992 
                                    New Zealand Timberlands Ltd 
                                                   0.0012189605 
                                   New Zealand Transport Agency 
                                                   0.0488861956 
                                           New Zealand Treasury 
                                                   0.0944211056 
                          New Zealand Underwater Heritage Group 
                                                   0.0111840626 
                          New Zealand Veterinary Pathology Ltd. 
                                                   0.0287478185 
                                        New Zealand Winegrowers 
                                                   0.0340077087 
                                         Newman Energy Research 
                                                   0.0148191986 
                                         Newtown Medical Centre 
                                                   0.0461819574 
                                                 NextWindow Ltd 
                                                   0.0461819574 
                                             Ngati Porou Hauora 
                                                   0.0255722930 
                                 Ngati Whakaue Tribal Lands Inc 
                                                   0.0069284140 
                                                Nielsen Company 
                                                   0.0273908222 
                                   NIU Development Incorporated 
                                                   0.0535592138 
                                                           NIWA 
                                                   0.3638731488 
                                             Norske Skog Tasman 
                                                   0.0249346566 
                            North Canterbury Veterinary Clinics 
                                                   0.0195312769 
                                            North Shore Hospice 
                                                   0.0474634045 
                              North Shore International Academy 
                                                   0.0278093065 
                            Northcott Research Consultants Ltd. 
                                                   0.0787596026 
                                        Northern Cancer Network 
                                                   0.0357429619 
                                  Northern Region IDEA Services 
                                                   0.0249346566 
                                     Northern Regional Alliance 
                                                   0.0138842432 
                         Northern Southland Veterinary Services 
                                                   0.0030384063 
                                Northland District Health Board 
                                                   0.1590355529 
                                     Northland Regional Council 
                                                   0.0735202199 
                                                       NorthTec 
                                                   0.0704160052 
                                             Novare Design Ltd. 
                                                   0.0148191986 
                                                   Numcore Ltd. 
                                                   0.0249346566 
                                                   Numinos Ltd. 
                                                   0.0249346566 
                                        Nurse Maude Association 
                                                   0.0603437647 
                                      Nutrigenomics New Zealand 
                                                   0.0807950034 
                               Nutrition Society of New Zealand 
                                                   0.0212473008 
                                                 NZ Oil and Gas 
                                                   0.0228447881 
                                        NZ Parsa Tiling Limited 
                                                   0.0148191986 
                                              NZFOCUS (NZ) Ltd. 
                                                   0.0249346566 
                                                    NZX Limited 
                                                   0.0249346566 
                                    O'Kane Consultants (NZ) Ltd 
                                                   0.0440321805 
                                                Oamaru Hospital 
                                                   0.0212473008 
                                                  Odyssey House 
                                                   0.0249346566 
               Office of the Health and Disability Commissioner 
                                                   0.0249346566 
   Office of the Parliamentary Commissioner for the Environment 
                                                   0.0395031204 
                                           Omahu Urology Clinic 
                                                   0.0291705251 
                                           OMV New Zealand Ltd. 
                                                   0.0556182741 
                                          Oncology Surgery Ltd. 
                                                   0.0445655922 
                                Open Polytechnic of New Zealand 
                                                   0.1254651930 
                                          OPRA Consulting Group 
                                                   0.0148284179 
                                        Optimal Clinical Trials 
                                                   0.0453398280 
                             Opus International Consultants Ltd 
                                                   0.1038084801 
                                             Oracle New Zealand 
                                                   0.0145768290 
                                             Oral Health Centre 
                                                   0.0320556060 
                                              Orange Consulting 
                                                   0.0212473008 
                                                  Orb Solutions 
                                                   0.0467293216 
                                     Organ Donation New Zealand 
                                                   0.0474634045 
                                            Oritain Global Ltd. 
                                                   0.0212473008 
                          Ornithological Society of New Zealand 
                                                   0.0473341831 
                                          Orokonui Ecosanctuary 
                                                   0.0358241298 
                                                          OSPRI 
                                                   0.0799331079 
                                        Otago Community Hospice 
                                                   0.0398993243 
                       Otago Computational Modelling Group Ltd. 
                                                   0.0548535325 
                                   Otago Daily Times Collective 
                                                   0.0212473008 
                                        Otago Girls High School 
                                                   0.0776629011 
                                                   Otago Museum 
                                                   0.0866294657 
                                              Otago Polytechnic 
                                                   0.1537147673 
                                         Otago Regional Council 
                                                   0.0562895940 
                                                Otahuhu College 
                                                   0.0571097128 
                                           Otakaro Pathways Ltd 
                                                   0.0191962510 
                                      Otorohanga Dental Surgery 
                                                   0.0212473008 
                                                 OTRS Group Ltd 
                                                   0.0516319471 
                                     Outome Management Services 
                                                   0.0249346566 
                                       P.N. Plimmer and Associ. 
                                                   0.0255722930 
                                    PA Handford and Assoc. Ltd. 
                                                   0.0094564741 
                                                 Pacific Brands 
                                                   0.0249346566 
                                Pacific Edge Biotechnology Ltd. 
                                                   0.0886180172 
             Pacific Health Research and Development Foundation 
                                                   0.0418387713 
                                        Pacific Radiology Group 
                                                   0.1243806845 
           Pacific Women's Health Research and Development Unit 
                                                   0.0498793202 
                                       Pakuranga Medical Centre 
                                                   0.0082863505 
                                          Palaecol Research Ltd 
                                                   0.0933223016 
                                  Palmerston North City Council 
                                                   0.0173363916 
                                  Palmerston North City Library 
                                                   0.0145768290 
                                                   Pansophy Ltd 
                                                   0.0356766685 
                                   Papamoa Pines Medical Centre 
                                                   0.0864889945 
                                            Paraparaumu College 
                                                   0.0602954152 
                                                  Paric Limited 
                                                   0.0249346566 
                                        Parkinson's New Zealand 
                                                   0.0249346566 
                                      Parresia Research Limited 
                                                   0.0249346566 
                                           Parsons Brinckerhoff 
                                                   0.0249346566 
                                    Pasifika Horizon Healthcare 
                                                   0.0249346566 
                                   Pasifika Medical Association 
                                                   0.0306534491 
                                          Pasifika Research Ltd 
                                                   0.0161383263 
                                                        Pathlab 
                                                   0.0377303774 
                                                 Patients First 
                                                   0.0243650995 
                               Paton-Simpson Associates Limited 
                                                   0.0329677433 
                                   Pattle Delamore Partners Ltd 
                                                   0.0161869526 
                                             Pegasus Health Ltd 
                                                   0.0767877909 
                                       Penny and Associates Ltd 
                                                   0.0511284497 
              Perinatal and Maternal Mortality Review Committee 
                                                   0.0704337275 
                                  Petersgate Counselling Centre 
                                                   0.0148191986 
                                       PF Olsen and Company Ltd 
                                                   0.0103299521 
                                       PGG Wrightson Seeds Ltd. 
                                                   0.0360872003 
                                                        PHARMAC 
                                                   0.0739195634 
                                             Pharmaceuticol Ltd 
                                                   0.0271904282 
                                  Pharmacy Guild of New Zealand 
                                                   0.0249346566 
                                      PharmTech Service Limited 
                                                   0.0486575964 
                 Philosophy of Education Society of Australasia 
                                                   0.0249346566 
                                        Photonz Corporation Ltd 
                                                   0.0249346566 
                                                    Pictor Ltd. 
                                                   0.0249346566 
                                                Pingar Research 
                                                   0.0111840626 
                                             Pinnacle Group Ltd 
                                                   0.0288352122 
                                               PipeTechnologies 
                                                   0.0270640959 
                                           Pipfruit New Zealand 
                                                   0.0352757922 
                                       Planning Consultants Ltd 
                                                   0.0367563556 
                                        Plant and Food Research 
                                                   0.3341419215 
                              Plant Protection Chemistry NZ Ltd 
                                                   0.0157330438 
                                              PlusGroup Limited 
                                                   0.0269208233 
                                                Pohatu Penguins 
                                                   0.0288339329 
                                                Polybatics Ltd. 
                                                   0.0314809437 
                                           Porirua City Council 
                                                   0.0212473008 
                                      Ports of Auckland Limited 
                                                   0.0255722930 
                                          Positive Thinking Ltd 
                                                   0.0249346566 
                                             Possum Observatory 
                                                   0.0970279870 
                                  Potter Building Services Ltd. 
                                                   0.0501704854 
                                                  Power Co Ltd. 
                                                   0.0249346566 
                      Power Systems Consultants New Zealand Ltd 
                                                   0.0016479868 
                                              PowerbyProxi Ltd. 
                                                   0.0249346566 
                                        Powerhouse Ventures Ltd 
                                                   0.0256837355 
                                    Practitioners First Limited 
                                                   0.0267575828 
                             Presbyterian Church of New Zealand 
                                                   0.0357429619 
                                  PriceWaterhouse Coopers (PwC) 
                                                   0.0664643664 
                               Priestley Structural Engineering 
                                                   0.0424605298 
                                    Private Endodontic Practice 
                                                   0.0212473008 
                                         ProCare Health Limited 
                                                   0.0583832284 
                                    Prohealth Physiotherapy Ltd 
                                                   0.0230702269 
                                                   Promisia Ltd 
                                                   0.0234461033 
                          Proteus Wildlife Research Consultants 
                                                   0.0459224042 
                                          Psychological Service 
                                                   0.0249346566 
                                              Psychology Centre 
                                                   0.0323214964 
                                        Pultron Composites Ltd. 
                                                   0.0178336058 
                                                        Pyrotek 
                                                   0.0213941598 
                                                     Q-Bit Ltd. 
                                                   0.0233707224 
                                                      QE Health 
                                                   0.0357429619 
                                                     Qnique Ltd 
                                                   0.0607587864 
                                           QStar Solutions Ltd. 
                                                   0.0180711659 
                                                      Quadradix 
                                                   0.0249346566 
                                       Quay Park Medical Centre 
                                                   0.0569902627 
                                          Queens Academic Group 
                                                   0.0249346566 
                                     Quest Integrity Group Ltd. 
                                                   0.0648212014 
                                         Quigley and Watts Ltd. 
                                                   0.0321118376 
                                   Quin Environmentals(NZ) Ltd. 
                                                   0.0338213194 
                                 Quintessence Developments Ltd. 
                                                   0.0172367328 
                                                     Quit Group 
                                                   0.0819954942 
                                  Radiata Pine Breeding Company 
                                                   0.0069284140 
                                      Radio Spectrum Management 
                                                   0.0301477514 
                                                     Rakon Ltd. 
                                                   0.0249346566 
                                       Rangiora New Life School 
                                                   0.0360664993 
                        Rape Prevention Education-Whakatu Mauri 
                                                   0.0535592138 
                            Rauawaawa Kaumatua Charitable Trust 
                                                   0.0535687972 
                                Raukatauri Music Therapy Centre 
                                                   0.0249346566 
                                  Raukura Hauora O Tainui Trust 
                                                   0.0226848532 
                                       Rayonier New Zealand Ltd 
                                                   0.0269223989 
                              Refugees as Survivors New Zealand 
                                                   0.0357429619 
                                  Reid Construction Systems Ltd 
                                                   0.0397538552 
                                               Renewable Energy 
                                                   0.0069284140 
                                                       Repromed 
                                                   0.0992710506 
                                    Reserve Bank of New Zealand 
                                                   0.0790194846 
                                        Resilient Organisations 
                                                   0.0397538552 
                       Resource Teacher: Learning and Behaviour 
                                                   0.0249346566 
                                          Revolution Fibres Ltd 
                                                   0.0626623983 
                                               Riccarton Rotary 
                                                   0.0000000000 
                        Risk Strategies Research and Consulting 
                                                   0.0170942902 
                                             Rivuli Development 
                                                   0.0111840626 
                                                RML Engineering 
                                                   0.0109051918 
                                         Roche Products Limited 
                                                   0.0357429619 
                                            Rockwell Automation 
                                                   0.0249346566 
                                    Rolleston Veterinary Clinic 
                                                   0.0599621860 
                                  Ropata Village Medical Centre 
                                                   0.0857164925 
                                 Rotorua General Practice Group 
                                                   0.0461819574 
                                       Rowe Davies Research Ltd 
                                                   0.0366550992 
      Royal Australian and New Zealand College of Psychiatrists 
                                                   0.0249346566 
        Royal Forest and Bird Protection Society of New Zealand 
                                                   0.0466907631 
             Royal New Zealand College of General Practitioners 
                                                   0.1050767416 
                              Royal New Zealand Plunket Society 
                                                   0.0996706514 
                                   Royal Society of New Zealand 
                                                   0.0635867235 
                      Ruaimoko Productions and Consultancy Ltd. 
                                                   0.0212473008 
                                                     Rumenz Ltd 
                                                   0.0305050676 
                                                      RuralLink 
                                                   0.0109051918 
 [ reached getOption("max.print") -- omitted 511 entries ]

$value
[1] 40.10482

$options
$options$bmat
[1] "I"

$options$n
[1] 1511

$options$which
[1] "LA"

$options$nev
[1] 1

$options$tol
[1] 0

$options$ncv
[1] 0

$options$ldv
[1] 0

$options$ishift
[1] 1

$options$maxiter
[1] 3000

$options$nb
[1] 1

$options$mode
[1] 1

$options$start
[1] 1

$options$sigma
[1] 0

$options$sigmai
[1] 0

$options$info
[1] 0

$options$iter
[1] 2

$options$nconv
[1] 1

$options$numop
[1] 30

$options$numopb
[1] 0

$options$numreo
[1] 21
top_10_eig1 <- tail(sort(eig1$vector), 10)
top_10_eig1
                       AgResearch    Auckland District Health Board  Canterbury District Health Board 
                        0.3760716                         0.4334652                         0.4357203 
            University of Waikato                    AUT University Victoria University of Wellington 
                        0.4373508                         0.4700463                         0.5846012 
         University of Canterbury                 Massey University               University of Otago 
                        0.5943213                         0.6779365                         0.8521192 
           University of Auckland 
                        1.0000000 
bottom_10_eig1 <- head(sort(eig1$vector), 10)
bottom_10_eig1
                            Alzheimers Northland                                  AP EnerTec Ltd. 
                                               0                                                0 
Aviation Industry Association of New Zealand Inc                            Bio Soil and Crop Ltd 
                                               0                                                0 
                                Blues Rugby Club                    Bruce Shallard and Associates 
                                               0                                                0 
                      ChangeMakers Refugee Forum                      Chatham Rock Phosphate Ltd. 
                                               0                                                0 
                      Chilton Saint James School                     Crown Fibre Holdings Limited 
                                               0                                                0 
eig2 <- eigen_centrality(net)
head(eig2)
$vector
                                       45 South Management Ltd. 
                                                   0.0051405189 
                                                     Abacus ALS 
                                                   0.0231551697 
                                                 AbacusBio Ltd. 
                                                   0.0356973370 
                                              ABB Power Quality 
                                                   0.0047352544 
                            ABI Rehabilitation New Zealand Ltd. 
                                                   0.0063161772 
                                         AC Research Associates 
                                                   0.0387233559 
                            Academic Colleges Group New Zealand 
                                                   0.0230236317 
                              Accident Compensation Corporation 
                                                   0.0908018610 
                       Action on Smoking and Health New Zealand 
                                                   0.0092094527 
                                                  Active Health 
                                                   0.0325944350 
                                      Acurity Health Group ltd. 
                                                   0.1227547002 
                                                Ade Consultants 
                                                   0.0460472634 
                                         Adidas Sports Medicine 
                                                   0.0230236317 
                                        Adis International Ltd. 
                                                   0.0192535471 
                                Advanced Clinical Skills Centre 
                                                   0.0568509437 
                                                          AECOM 
                                                   0.0462858055 
                                                      AECS Ltd. 
                                                   0.0087353529 
                                                  Aerocool Ltd. 
                                                   0.0043676764 
                                                  Aeroqual Ltd. 
                                                   0.0417272451 
                                              Affinity Services 
                                                   0.0460472634 
                                        AFT Pharmaceuticals Ltd 
                                                   0.0447142640 
                                             AFTpharmaceuticals 
                                                   0.0460472634 
                                  Agencies for Nutrition Action 
                                                   0.0323759262 
                                Agile Utilities New Zealand Ltd 
                                                   0.0186176938 
                                               Agknowledge Ltd. 
                                                   0.0138076338 
                                                     AgResearch 
                                                   0.1295355263 
                                             Agri-Optic NZ Ltd. 
                                                   0.0186176938 
                                             Agribusiness Group 
                                                   0.0357889155 
                                    AgriGenesis Biosciences Ltd 
                                                   0.0155277450 
                                          AgriHealth NZ Limited 
                                                   0.0003791672 
                                        Agrimm Technologies Ltd 
                                                   0.0014114278 
                                                AgriNova NZ Ltd 
                                                   0.0034342151 
                                            AgriQuality Limited 
                                                   0.0024519060 
                                         Agvance Marketing Ltd. 
                                                   0.0122912251 
                                                Air New Zealand 
                                                   0.0448256895 
                                               Air Quality Ltd. 
                                                   0.0479686889 
                                            Airborne Honey Ltd. 
                                                   0.0178906864 
                                          Akaroa Medical Centre 
                                                   0.0308851034 
  Ako Aotearoa National Centre for Tertiary Teaching Excellence 
                                                   0.0033343580 
                              Akoranga Integrated Health Clinic 
                                                   0.0091741574 
                                       Alan Bell and Associates 
                                                   0.0150891395 
                       Albany Basin Accident and Medical Centre 
                                                   0.0057390827 
                        Alcohol Advisory Council of New Zealand 
                                                   0.0033898578 
                       Alcohol Harm Minimisation Advisory Group 
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                                      Alcohol Healthwatch Trust 
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                                       Alexandra Medical Centre 
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                                              Alfriston College 
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                               Allan Planning and Research Ltd. 
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      Allen & Clarke  Policy and Regulatory Specialists Limited 
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                                                      Alphalabs 
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                         Alpine and Polar Processes Consultancy 
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                                           Alzheimers Northland 
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                        Amalgamates Solutions and Research Ltd. 
                                                   0.0076372971 
                                            Amity Health Centre 
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                                        Ancare New Zealand Ltd. 
                                                   0.0154425517 
                                          Ancare Scientific Ltd 
                                                   0.0148012613 
                                                      Anexa FVC 
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                                Anglesea Medical Properties Ltd 
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                                          Animal Dermatology NZ 
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                                Animal Health Board New Zealand 
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         Animals and Marine Surveillance and Investigation Team 
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                                     Animation Research Limited 
                                                   0.0308851034 
                                       Antarctic Heritage Trust 
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                                         Antarctica New Zelaand 
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                                  Antarctica Scientific Limited 
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                                     Antipodean Pharmaceuticals 
                                                   0.0514852405 
                                    Aorangi Veterinary Services 
                                                   0.0023364362 
                                           Aotea Pathology Ltd. 
                                                   0.0798343978 
               Aotearoa Alcohol and Other Drug Consumer Network 
                                                   0.0393726856 
                                                AP EnerTec Ltd. 
                                                   0.0000000000 
                              Applied Engineering Research Ltd. 
                                                   0.0039634640 
                         Applied Research and Technologies Ltd. 
                                                   0.0062097830 
                        Applied Research Associates New Zealand 
                                                   0.0071538796 
                                       AquaBio Consultants Ltd. 
                                                   0.0081432486 
                                        Aquaculture New Zealand 
                                                   0.0426818114 
                                         Aqualinc Research Ltd. 
                                                   0.0690067072 
                                        Aquanet Consulting Ltd. 
                                                   0.0186176938 
                                Aquatic Research Solutions Ltd. 
                                                   0.0237424298 
                                             Aranui High School 
                                                   0.0077470596 
                                                  ARANZ Geo Ltd 
                                                   0.0071538796 
                                         ARANZ Medical Scanning 
                                                   0.0083697771 
                                                 Areograph Ltd. 
                                                   0.0332527306 
                                               ARH Construction 
                                                   0.0460472634 
                                                Aroa Biosurgery 
                                                   0.1138977058 
                                               Arohanui Hospice 
                                                   0.0011343690 
                                        Arotec Diagnostics Ltd. 
                                                   0.0186770932 
                                              Ascot Angiography 
                                                   0.0263744519 
                     Ascot Women's Cancer Centre of New Zealand 
                                                   0.0017815247 
                                    Asia New Zealand Foundation 
                                                   0.0602268311 
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                                                   0.0071028817 
                                Aspiring Veterinary Service Ltd 
                                                   0.0211938675 
                    ASR Limited Martine Consulting and Research 
                                                   0.0274945136 
                                     Assa Abloy New Zealand Ltd 
                                                   0.0308851034 
                                      Assistive Technology Ltd. 
                                                   0.0186176938 
                                        Assurity Consulting Ltd 
                                                   0.0045870787 
                                                   AsureQuality 
                                                   0.0362800019 
                                              AsureQuality Ltd. 
                                                   0.0260401584 
                                                    At the Vets 
                                                   0.0197859118 
                                 Atkinson and Rapley Consulting 
                                                   0.0093088469 
                                            Atlantis HealthCare 
                                                   0.0460472634 
                         Auckland-Waikato Fish and Game Council 
                                                   0.0133374320 
                                  Auckland Astronomical Society 
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                                       Auckland Botanic Gardens 
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                                         Auckland Breast Centre 
                                                   0.0057390827 
                                          Auckland City Mission 
                                                   0.0825744675 
                                 Auckland Clinical Studies Ltd. 
                                                   0.0769368983 
                                               Auckland Council 
                                                   0.1164176955 
                                      Auckland Cricket Assn Inc 
                                                   0.0091741574 
                                           Auckland Dermatology 
                                                   0.0063161772 
                                 Auckland District Health Board 
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                                                   Auckland Eye 
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                                           Auckland Heart Group 
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                                  Auckland Institute of Studies 
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                         Auckland International Airport Limited 
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                                                Auckland Museum 
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                           Auckland Refugee Community Coalition 
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                                      Auckland Regional Council 
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                         Auckland Southern Cross Hospital Group 
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                                             Auckland Transport 
                                                   0.0460472634 
                                                   Auckland Zoo 
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                                                        Aurecon 
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            Australian and New Zealand College of Anaesthetists 
                                                   0.0338273120 
                                                 AUT University 
                                                   0.1992334997 
                                          Automation Design Ltd 
                                                   0.0030373531 
               Aviation Industry Association of New Zealand Inc 
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                                                     Avivet Ltd 
                                                   0.0152736034 
                                       Avocado Industry Council 
                                                   0.0049038121 
                                        Babbage Consulting Ltd. 
                                                   0.0703392860 
                                Ballance Agri-Nutrients Limited 
                                                   0.0332383217 
                                               Bank of Scotland 
                                                   0.0460472634 
                                              Bartonk Solutions 
                                                   0.0055011600 
                                 Batten Animal Research Network 
                                                   0.0210882627 
                                      Baxter Healthcare Limited 
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                                                  Bay Audiology 
                                                   0.0047352544 
                            Bay of Plenty District Health Board 
                                                   0.0747680534 
                                      Bay of Plenty Polytechnic 
                                                   0.0747402583 
                                 Bay of Plenty Regional Council 
                                                   0.0378856517 
                                                    Bay Urology 
                                                   0.0171981126 
                                  Bayer CropScience New Zealand 
                                                   0.0061878771 
                                      Bayleys Property Services 
                                                   0.0460472634 
                                             BC Consulting Ltd. 
                                                   0.0032060228 
                                            BCRL Energy Limited 
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                                                           Beca 
                                                   0.0782501365 
                                      Beef and Lamb New Zealand 
                                                   0.0995252040 
                                             Bennett Scientific 
                                                   0.0488886893 
                                           Benthic Science Ltd. 
                                                   0.0227041495 
                                                 Berryworld Ltd 
                                                   0.0083411103 
                                  Best Practice Advocacy Centre 
                                                   0.0504594210 
                                                 Beta Solutions 
                                                   0.0646649572 
                                                  Bethesda Care 
                                                   0.0287627144 
                                        Betta Bees Research Ltd 
                                                   0.0308851034 
                                      Better Border Biosecurity 
                                                   0.0103878326 
                                      BHU Future Farming Centre 
                                                   0.0198514744 
                                       Bickler Consultants Ltd. 
                                                   0.0395269924 
                                                         BikeNZ 
                                                   0.0142057633 
                                          Bio Soil and Crop Ltd 
                                                   0.0000000000 
                                Bioactives Research New Zealand 
                                                   0.0393679157 
                                  Biodiscovery New Zealand Ltd. 
                                                   0.0230018794 
                                                 Biomarine Ltd. 
                                                   0.0460472634 
                                                Biomatters Ltd. 
                                                   0.0539087351 
                                         Biometrics Matters Ltd 
                                                   0.0358754961 
                                         Biopolymer Network Ltd 
                                                   0.0554100925 
                                        Biosecurity New Zealand 
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                                BioSylve Forest Science NZ Ltd. 
                                                   0.0039634640 
                              BirdLife Global Seabird Programme 
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                                               Blind Foundation 
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                                         BLIS Technologies Ltd. 
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                                     Blue Water Marine Research 
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                                               Blues Rugby Club 
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                                             Bodeker Scientific 
                                                   0.0499122626 
                                            Body Aid Clinic Ltd 
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                                              Boffa Miskell Ltd 
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                                         Bomac Laboratories Ltd 
                                                   0.0478457679 
                                              Boulcott Hospital 
                                                   0.0031020184 
                                               Braemar Hospital 
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                                                     BRANZ Ltd. 
                                                   0.0510072266 
                                       Bream Bay Medical Centre 
                                                   0.0460472634 
                             Breast Care and Screening Services 
                                                   0.0523634406 
                        Breast Surgeons' Society of New Zealand 
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                                               Breen Consulting 
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                   Brian Ricketts Geological Consulting Limited 
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                                        Broadway Medical Centre 
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                                       Broadway Surgical Clinic 
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                                           Broken Hills Gold Co 
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                                                   0.0054840206 
                                   Cadwallader Tree Consultancy 
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                                         Cahill Animal Hospital 
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                                     CAL Engineering Management 
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                                           Callaghan Innovation 
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                                               Cambridge Clinic 
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                                  Cambridge Veterinary Services 
                                                   0.0087018909 
                                         Cameron Medical Clinic 
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                                   Campbell and Associates Ltd. 
                                                   0.0049038121 
                          Cancer Control Council of New Zealand 
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                                  Cancer Society of New Zealand 
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                              Canterbury Charity Hospital Trust 
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        Canterbury Civil Defence and Emergency Management Group 
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                               Canterbury District Health Board 
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                       Canterbury Earthquake Recovery Authority 
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                                          Canterbury Health Ltd 
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                                     Canterbury Medical Imaging 
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                                              Canterbury Museum 
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                  Canterbury Rugby Football Union and Crusaders 
                                                   0.0083462461 
                                      CanZealand Geoscience Ltd 
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              Cape Kidnappers and Ocean Beach Wildlife Preserve 
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                                                 Cape Sanctuary 
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                        Capital and Coast District Health Board 
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                                        Capital Eye Specialists 
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                                               Capital Research 
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                                             Carbon Partnership 
                                                   0.0054840206 
                                Cardiac Inherited Disease Group 
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                                    Care of Orca Research Trust 
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                                          Carey Baptist College 
                                                   0.0460472634 
                                         Carroll Consulting ltd 
                                                   0.0210014960 
                                         Carson Associates Ltd. 
                                                   0.0039634640 
                                        Carter Holt Harvey Ltd. 
                                                   0.0510266532 
                                    Carter National Observatory 
                                                   0.0298089593 
                                                Cashmere Health 
                                                   0.0158064741 
                                                     Catch Ltd. 
                                                   0.0460472634 
                                                         Catmed 
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                                             Cawthron Institute 
                                                   0.0946198276 
                                    CBG Health Research Limited 
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                                              Centennial Health 
                                                   0.0340179725 
                               Center for Backyard Astrophysics 
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          Central and Southern New Zealand Craniofacial Program 
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                                              Central City Vets 
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                                          Central Otago Tourism 
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                                         Central Stories Museum 
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                                                     CentralMed 
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                               Centre for Backyard Astrophysics 
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            Centre for Clinical Research and Effective Practice 
                                                   0.0514017654 
                                    Centre for Dairy Excellence 
                                                   0.0195163691 
              Centre for Minerals Environmental Research (CMER) 
                                                   0.0322017746 
           Centre for Research Evaluation and Social Assessment 
                                                   0.0024621169 
                      Centre for Youth Health in South Auckland 
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                                              CH and Associates 
                                                   0.0199705401 
                                     ChangeMakers Refugee Forum 
                                                   0.0000000000 
                                    Chatham Rock Phosphate Ltd. 
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                                              Chemipreneur Ltd. 
                                                   0.0332762804 
                                       Chemistry Communications 
                                                   0.0287627144 
                                   Chiefs Super Rugby Franchise 
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                                         Child and Youth Health 
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                                     Child Poverty Action Group 
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                                     Chilton Saint James School 
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                                                   Chiptech Ltd 
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                                      Christchurch City Council 
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                         Christchurch Emergency Care Foundation 
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               Christchurch Polytechnic Institute of Technology 
                                                   0.0586470274 
                             Christchurch Psychologists' Office 
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                                    Christchurch Vascular Group 
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                                                  City Care Ltd 
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                                                   City Fitness 
                                                   0.0552771119 
                                       Civil Aviation Authority 
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                                                          Claro 
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                                     ClearSight Consultants Ltd 
                                                   0.0726772875 
                                     Clement and Associates Ltd 
                                                   0.0114933824 
                    Clendon Burns and Park Consulting Engineers 
                                                   0.0099684125 
                                               CLIMsystems Ltd. 
                                                   0.0043676764 
                                              Clinical Horizons 
                                                   0.0440184504 
                                               Clinical Systems 
                                                   0.0063944324 
                                  Clutha Veterinary Association 
                                                   0.0332215396 
                                        Coast and Catchment Ltd 
                                                   0.0404210536 
                                   Coast to Coast Health Centre 
                                                   0.0057390827 
                                Coastal and Aquatic Systems Ltd 
                                                   0.0740056293 
                                      Coastal Systems (NZ) Ltd. 
                                                   0.0046167379 
                                          Coastline Consultants 
                                                   0.0039634640 
                                    Cognition Education Limited 
                                                   0.0153490878 
                                                       Cognosco 
                                                   0.0161886645 
                                          Colgate-Palmolive Ltd 
                                                   0.0142057633 
                                           Colin Christian Ltd. 
                                                   0.0308851034 
                                          Collins Carriers Ltd. 
                                                   0.0056457110 
                                                 Colmar Brunton 
                                                   0.0460472634 
                                                Columba College 
                                                   0.0308851034 
                                              Common Ground Ltd 
                                                   0.0274942182 
                                       Commtest Instruments Ltd 
                                                   0.0142057633 
           Community Clinic for Sexual Health and Contraception 
                                                   0.0460472634 
                                  Compac Sorting Equipment Ltd. 
                                                   0.0509510755 
                                            Compac Technologies 
                                                   0.0186176938 
                                                 Compass Health 
                                                   0.0279327199 
                                  Compusoft Engineering Limited 
                                                   0.0460472634 
                                     Compusoft Engineering Ltd. 
                                                   0.0251974095 
                                             Comtel System Ltd. 
                                                   0.0192843263 
                                       Comvita New Zealand Ltd. 
                                                   0.0229004554 
                                           Connectos Consulting 
                                                   0.0608228747 
                                               Connovation Ltd. 
                                                   0.0484272023 
                      Conservation and Environmental Management 
                                                   0.0176382812 
                                   Construction Techniques Ltd. 
                                                   0.0602530267 
                                     Consulting Dietitians Ltd. 
                                                   0.0338273120 
                                            Contact Energy Ltd. 
                                                   0.0133479861 
                                        Contract Landscapes Ltd 
                                                   0.0046167379 
                                            CORE Education Ltd. 
                                                   0.0259354160 
                                                       Cosgrove 
                                                   0.0142057633 
                         Counties Manukau District Health Board 
                                                   0.1388667186 
                                                      Covec Ltd 
                                                   0.0797552223 
                                           CPG New Zealand Ltd. 
                                                   0.0186176938 
                                        Crawford Medical Centre 
                                                   0.0251974095 
                                                CRL Energy Ltd. 
                                                   0.0285939087 
                                               Cromwell College 
                                                   0.0133374320 
                                         Cropmark Seeds Limited 
                                                   0.0148377240 
                                   Crown Fibre Holdings Limited 
                                                   0.0000000000 
                                CURT St George's Medical Centre 
                                                   0.1088339740 
                                       Cuttriss Consultants Ltd 
                                                   0.0065392413 
                                        Cymbiotix Group Limited 
                                                   0.0552214209 
                                                    Cyperus Ltd 
                                                   0.0681144984 
                                         Dairy Consultants Ltd. 
                                                   0.0032826090 
                              Dairy Goat Co-operative (NZ) Ltd. 
                                                   0.0465849078 
                                  Dairy Production Systems Ltd. 
                                                   0.0002752443 
                                                        DairyNZ 
                                                   0.0784106113 
                                    David Butler Associates Ltd 
                                                   0.0186176938 
                                    Davidson Environmental Ltd. 
                                                   0.0819055933 
                                                 DaVinci Clinic 
                                                   0.0019976835 
                                       DCM Process Control Ltd. 
                                                   0.0460472634 
                             DEA Research Software Surgery Ltd. 
                                                   0.0460472634 
                                            Deepwater Group Ltd 
                                                   0.0114933824 
                                                         DeerNZ 
                                                   0.0049038121 
                                                       Deloitte 
                                                   0.1097558239 
                                     Department of Conservation 
                                                   0.1478014695 
                                      Department of Corrections 
                                                   0.0142057633 
                                             Development Action 
                                                   0.0133374320 
                                          Development By Design 
                                                   0.0133374320 
                                           Devon Medical Centre 
                                                   0.0049977405 
                                      DHI Water and Environment 
                                                   0.0041031253 
                                             Diabetes Otago Inc 
                                                   0.0308851034 
                                          Diagnostic Laboratory 
                                                   0.0402217443 
                                              Diagnostic Medlab 
                                                   0.0576565345 
                                      Digestive Health Services 
                                                   0.0406815603 
                                        Digital Sensing Limited 
                                                   0.0197948985 
                                             Disability Connect 
                                                   0.0482699631 
                                     Disability Resource Centre 
                                                   0.0608228747 
                                                   Diversity NZ 
                                                   0.0608228747 
                                                 DM Consultants 
                                                   0.0636283979 
                                           DNA Investments Ltd. 
                                                   0.0044249022 
                          Dnature diagnostics and research Ltd. 
                                                   0.0604438840 
                                  Doctors for Sexual Abuse Care 
                                                   0.0098038017 
                                            Donaghys Industries 
                                                   0.0051405189 
                                       Donald Beasley Institute 
                                                   0.0513084063 
                                    Dorothy-Jean and Associates 
                                                   0.0059029423 
                                                  Dovedale Ltd. 
                                                   0.0862412137 
                                       Downer EDI Works Limited 
                                                   0.0127183613 
                                      Dr. Malcolm McKellar Ltd. 
                                                   0.0026601840 
                                                 Dragonfly Ltd. 
                                                   0.0398691754 
                            Drummond Food Science Advisory Ltd. 
                                                   0.0308851034 
                                           Dumpark Data Science 
                                                   0.0005298051 
                                               Duncan Cotterill 
                                                   0.0175662940 
                                           Dunedin City Council 
                                                   0.0334516992 
                                     Dunedin Heat Pumps Limited 
                                                   0.0308851034 
                                Dunedin South Veterinary Clinic 
                                                   0.0186176938 
                              Dunning Thornton Consultants Ltd. 
                                                   0.0506640013 
                                          Dynamic Controls Ltd. 
                                                   0.0141326860 
                                                       Dynatest 
                                                   0.0519614827 
                         Dyspraxia Support Group of New Zealand 
                                                   0.0406815603 
                                          Earthquake Commission 
                                                   0.0774697252 
                                   Earthtech Consulting Limited 
                                                   0.0482699631 
                                Eastern Institute of Technology 
                                                   0.1029689503 
                                   Eastern Region Fish and Game 
                                                   0.0119179126 
              Eastern Suburbs Association Football Club (ESAFC) 
                                                   0.0646649572 
                              Eastland Veterinary Services Ltd. 
                                                   0.0209541299 
                                       Eaton Power Quality Ltd. 
                                                   0.0035514408 
                                                ECG Consultants 
                                                   0.0186176938 
                        Eco-Vista Photography and Research Ltd. 
                                                   0.0675821239 
                                                 Eco Nomos Ltd. 
                                                   0.0132263543 
                                    Eco Research Associates Ltd 
                                                   0.0840869064 
                                                 ECoast Limited 
                                                   0.0115056815 
                                      EcoGecko Consultants Ltd. 
                                                   0.0410698575 
                                     Ecosynergy Group Ltd (EGL) 
                                                   0.0133374320 
                                                      Ectus Ltd 
                                                   0.0087353529 
                           Edmund Lawler and Associates Limited 
                                                   0.0133374320 
                                                Education House 
                                                   0.0000000000 
                                        Education Review Office 
                                                   0.0460472634 
                                 Educational Leadership Project 
                                                   0.0087353529 
                                          Electricity Authority 
                                                   0.0575959558 
                    Eli Lilly and Company (New Zealand) Limited 
                                                   0.0549214843 
                                           Elmwood Orthopaedics 
                                                   0.0332350417 
                            Eltham District Veterinary Services 
                                                   0.0218472177 
                                             Endoscopy Auckland 
                                                   0.0485546450 
                   Energy Efficiency and Conservation Authority 
                                                   0.0587375573 
                                 Energy Solution Providers Ltd. 
                                                   0.0056457110 
                                                    EnForm Tech 
                                                   0.0108447368 
                                         Enigma Publishing Ltd. 
                                                   0.0552493766 
                                                      Ensys Ltd 
                                                   0.0071028817 
                                                   Entecol Ltd. 
                                                   0.0364694794 
                                     Enviro-Mark Solutions Ltd. 
                                                   0.0142057633 
                                                Enviro Research 
                                                   0.0062526751 
                                         Environment Canterbury 
                                                   0.1051682495 
                          Environment Protection Authority(EPA) 
                                                   0.0251870864 
                              Environmental Management Services 
                                                   0.0065392413 
                                  Environmental Restoration Ltd 
                                                   0.0039634640 
                                    ENZO Nutraceuticals Limited 
                                                   0.0432330434 
                                                Epi-interactive 
                                                   0.0467923996 
                                     Epsom Girls Grammar School 
                                                   0.0230236317 
                                      Equine Health Association 
                                                   0.0044249022 
                                                    ERA Ecology 
                                                   0.0570685119 
                                                      Erin Park 
                                                   0.0387233559 
                                                            ESR 
                                                   0.1281931180 
                                            Etec Crop Solutions 
                                                   0.0049038121 
                                     Eudyptes EcoConsulting Ltd 
                                                   0.0376909566 
                                                     Explore NZ 
                                                   0.0186176938 
                                                  Eye Institute 
                                                   0.0568509437 
                                     Far North District Council 
                                                   0.0252433140 
                                          Farm Cove Observatory 
                                                   0.0130408739 
                                        Feilding Medical Centre 
                                                   0.0617973474 
                                                       FEM Ltd. 
                                                   0.0000000000 
                                       Fern Research Foundation 
                                                   0.0151686834 
                                                Ferndale School 
                                                   0.0142057633 
                                           Fertility Associates 
                                                   0.0467351163 
                                    Financial Markets Authority 
                                                   0.0133374320 
                                               Fish and Game NZ 
                                                   0.0195336557 
                                   Fisher and Paykel Appliances 
                                                   0.0460472634 
                              Fisher and Paykel Healthcare Ltd. 
                                                   0.1051717710 
                        Fishing Vessel Management Services Ltd. 
                                                   0.0106868995 
                                            FitzRoy of Merivale 
                                                   0.0196897839 
                                       Fletcher Construction Co 
                                                   0.0525226591 
                                                  FMR GROUP LTD 
                                                   0.0062108748 
                                                       Fonterra 
                                                   0.0781241575 
                              Food and Bio-based Products Group 
                                                   0.0139258291 
                                          Food and Health Group 
                                                   0.0201774155 
                                Foot Science International Ltd. 
                                                   0.0308851034 
                            Forensic and Industrial Science Ltd 
                                                   0.0230236317 
                                                Forest and Bird 
                                                   0.0635109105 
                                             Forever Beech Ltd. 
                                                   0.0142057633 
                                 Foundation for Arable Research 
                                                   0.0087407843 
                 Foundation for Research Science and Technology 
                                                   0.0186176938 
                        Fox and Associates-Consulting Surveyors 
                                                   0.0207450047 
                                        Fred Hollows Foundation 
                                                   0.0542152213 
  Fresenius Medical Care Australia Pty Ltd (New Zealand Branch) 
                                                   0.0524416958 
                                               Freshport NZ Ltd 
                                                   0.0056457110 
                                           Frontier Global Ltd. 
                                                   0.0460472634 
                                              Fruitfed Supplies 
                                                   0.0033567474 
                                          Fruition Horticulture 
                                                   0.0213326267 
                                              FullSpectrum Ltd. 
                                                   0.0087353529 
                                              Fulton Hogan Ltd. 
                                                   0.0281771669 
                                        Future Forests Research 
                                                   0.0039634640 
                                                   Future Steps 
                                                   0.0911381301 
                                            FuturebyDesign Ltd. 
                                                   0.0642077847 
                                                FutureMATH Ltd. 
                                                   0.0009506246 
                            Gallagher Animal Management Systems 
                                                   0.0087353529 
                                              Gambling Helpline 
                                                   0.0277918512 
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                                                         Google 
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                            Intus Digestive and Colorectal Care 
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                                              IZON Science Ltd. 
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                         Levin and Horowhenua Veterinary Centre 
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                                          Lincoln Agritech Ltd. 
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                                                        Lowe NZ 
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                        Mental Health Foundation of New Zealand 
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New Zealand School Acupuncture and Traditional Chinese Medicine 
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                                           New Zealand Treasury 
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                          New Zealand Underwater Heritage Group 
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                                                Nielsen Company 
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                                     Northern Regional Alliance 
                                                   0.0066771905 
                         Northern Southland Veterinary Services 
                                                   0.0034761237 
                                Northland District Health Board 
                                                   0.0879586046 
                                     Northland Regional Council 
                                                   0.0934007545 
                                                       NorthTec 
                                                   0.0443143317 
                                             Novare Design Ltd. 
                                                   0.0142057633 
                                                   Numcore Ltd. 
                                                   0.0460472634 
                                                   Numinos Ltd. 
                                                   0.0460472634 
                                        Nurse Maude Association 
                                                   0.0275129369 
                                      Nutrigenomics New Zealand 
                                                   0.0367598254 
                               Nutrition Society of New Zealand 
                                                   0.0154425517 
                                                 NZ Oil and Gas 
                                                   0.0198766733 
                                        NZ Parsa Tiling Limited 
                                                   0.0142057633 
                                              NZFOCUS (NZ) Ltd. 
                                                   0.0230236317 
                                                    NZX Limited 
                                                   0.0460472634 
                                    O'Kane Consultants (NZ) Ltd 
                                                   0.0602226717 
                                                Oamaru Hospital 
                                                   0.0154425517 
                                                  Odyssey House 
                                                   0.0230236317 
               Office of the Health and Disability Commissioner 
                                                   0.0460472634 
   Office of the Parliamentary Commissioner for the Environment 
                                                   0.0230406528 
                                           Omahu Urology Clinic 
                                                   0.0366594181 
                                           OMV New Zealand Ltd. 
                                                   0.0511029676 
                                          Oncology Surgery Ltd. 
                                                   0.0408721696 
                                Open Polytechnic of New Zealand 
                                                   0.0834906228 
                                          OPRA Consulting Group 
                                                   0.0142359485 
                                        Optimal Clinical Trials 
                                                   0.0398952216 
                             Opus International Consultants Ltd 
                                                   0.0645022699 
                                             Oracle New Zealand 
                                                   0.0133374320 
                                             Oral Health Centre 
                                                   0.0416887837 
                                              Orange Consulting 
                                                   0.0308851034 
                                                  Orb Solutions 
                                                   0.0529578883 
                                     Organ Donation New Zealand 
                                                   0.0353269255 
                                            Oritain Global Ltd. 
                                                   0.0308851034 
                          Ornithological Society of New Zealand 
                                                   0.0549868177 
                                          Orokonui Ecosanctuary 
                                                   0.0442225354 
                                                          OSPRI 
                                                   0.0706606939 
                                        Otago Community Hospice 
                                                   0.0476574625 
                       Otago Computational Modelling Group Ltd. 
                                                   0.0496956693 
                                   Otago Daily Times Collective 
                                                   0.0308851034 
                                        Otago Girls High School 
                                                   0.1088874926 
                                                   Otago Museum 
                                                   0.0553771184 
                                              Otago Polytechnic 
                                                   0.0557382910 
                                         Otago Regional Council 
                                                   0.0351789362 
                                                Otahuhu College 
                                                   0.0581531258 
                                           Otakaro Pathways Ltd 
                                                   0.0147002690 
                                      Otorohanga Dental Surgery 
                                                   0.0308851034 
                                                 OTRS Group Ltd 
                                                   0.0602159741 
                                     Outome Management Services 
                                                   0.0460472634 
                                       P.N. Plimmer and Associ. 
                                                   0.0482699631 
                                    PA Handford and Assoc. Ltd. 
                                                   0.0070008171 
                                                 Pacific Brands 
                                                   0.0230236317 
                                Pacific Edge Biotechnology Ltd. 
                                                   0.0998157607 
             Pacific Health Research and Development Foundation 
                                                   0.0416413255 
                                        Pacific Radiology Group 
                                                   0.0852379945 
           Pacific Women's Health Research and Development Unit 
                                                   0.0683734936 
                                       Pakuranga Medical Centre 
                                                   0.0033515457 
                                          Palaecol Research Ltd 
                                                   0.0506475414 
                                  Palmerston North City Council 
                                                   0.0101877423 
                                  Palmerston North City Library 
                                                   0.0133374320 
                                                   Pansophy Ltd 
                                                   0.0220982646 
                                   Papamoa Pines Medical Centre 
                                                   0.0928809741 
                                            Paraparaumu College 
                                                   0.0523040361 
                                                  Paric Limited 
                                                   0.0460472634 
                                        Parkinson's New Zealand 
                                                   0.0230236317 
                                      Parresia Research Limited 
                                                   0.0460472634 
                                           Parsons Brinckerhoff 
                                                   0.0460472634 
                                    Pasifika Horizon Healthcare 
                                                   0.0460472634 
                                   Pasifika Medical Association 
                                                   0.0516262885 
                                          Pasifika Research Ltd 
                                                   0.0083367517 
                                                        Pathlab 
                                                   0.0433833264 
                                                 Patients First 
                                                   0.0191624112 
                               Paton-Simpson Associates Limited 
                                                   0.0400592608 
                                   Pattle Delamore Partners Ltd 
                                                   0.0164941129 
                                             Pegasus Health Ltd 
                                                   0.0642293445 
                                       Penny and Associates Ltd 
                                                   0.0663179375 
              Perinatal and Maternal Mortality Review Committee 
                                                   0.0707548700 
                                  Petersgate Counselling Centre 
                                                   0.0142057633 
                                       PF Olsen and Company Ltd 
                                                   0.0088351016 
                                       PGG Wrightson Seeds Ltd. 
                                                   0.0258262532 
                                                        PHARMAC 
                                                   0.0438168198 
                                             Pharmaceuticol Ltd 
                                                   0.0363256511 
                                  Pharmacy Guild of New Zealand 
                                                   0.0460472634 
                                      PharmTech Service Limited 
                                                   0.0396344015 
                 Philosophy of Education Society of Australasia 
                                                   0.0460472634 
                                        Photonz Corporation Ltd 
                                                   0.0460472634 
                                                    Pictor Ltd. 
                                                   0.0460472634 
                                                Pingar Research 
                                                   0.0047800509 
                                             Pinnacle Group Ltd 
                                                   0.0508646209 
                                               PipeTechnologies 
                                                   0.0525226591 
                                           Pipfruit New Zealand 
                                                   0.0280166654 
                                       Planning Consultants Ltd 
                                                   0.0574269711 
                                        Plant and Food Research 
                                                   0.1064951902 
                              Plant Protection Chemistry NZ Ltd 
                                                   0.0035163776 
                                              PlusGroup Limited 
                                                   0.0145858096 
                                                Pohatu Penguins 
                                                   0.0203458204 
                                                Polybatics Ltd. 
                                                   0.0128746139 
                                           Porirua City Council 
                                                   0.0308851034 
                                      Ports of Auckland Limited 
                                                   0.0482699631 
                                          Positive Thinking Ltd 
                                                   0.0230236317 
                                             Possum Observatory 
                                                   0.0069860932 
                                  Potter Building Services Ltd. 
                                                   0.0695687692 
                                                  Power Co Ltd. 
                                                   0.0460472634 
                      Power Systems Consultants New Zealand Ltd 
                                                   0.0007332456 
                                              PowerbyProxi Ltd. 
                                                   0.0092094527 
                                        Powerhouse Ventures Ltd 
                                                   0.0168993386 
                                    Practitioners First Limited 
                                                   0.0498031771 
                             Presbyterian Church of New Zealand 
                                                   0.0568509437 
                                  PriceWaterhouse Coopers (PwC) 
                                                   0.0871589088 
                               Priestley Structural Engineering 
                                                   0.0638562314 
                                    Private Endodontic Practice 
                                                   0.0308851034 
                                         ProCare Health Limited 
                                                   0.0402932634 
                                    Prohealth Physiotherapy Ltd 
                                                   0.0191984654 
                                                   Promisia Ltd 
                                                   0.0336423765 
                          Proteus Wildlife Research Consultants 
                                                   0.0129373969 
                                          Psychological Service 
                                                   0.0460472634 
                                              Psychology Centre 
                                                   0.0293398089 
                                        Pultron Composites Ltd. 
                                                   0.0021164695 
                                                        Pyrotek 
                                                   0.0087282370 
                                                     Q-Bit Ltd. 
                                                   0.0198514744 
                                                      QE Health 
                                                   0.0568509437 
                                                     Qnique Ltd 
                                                   0.0902697988 
                                           QStar Solutions Ltd. 
                                                   0.0043343552 
                                                      Quadradix 
                                                   0.0460472634 
                                       Quay Park Medical Centre 
                                                   0.0823342069 
                                          Queens Academic Group 
                                                   0.0230236317 
                                     Quest Integrity Group Ltd. 
                                                   0.0270054146 
                                         Quigley and Watts Ltd. 
                                                   0.0252390086 
                                   Quin Environmentals(NZ) Ltd. 
                                                   0.0343539908 
                                 Quintessence Developments Ltd. 
                                                   0.0178906864 
                                                     Quit Group 
                                                   0.0529746407 
                                  Radiata Pine Breeding Company 
                                                   0.0009908660 
                                      Radio Spectrum Management 
                                                   0.0276791693 
                                                     Rakon Ltd. 
                                                   0.0153490878 
                                       Rangiora New Life School 
                                                   0.0379879851 
                        Rape Prevention Education-Whakatu Mauri 
                                                   0.0385538603 
                            Rauawaawa Kaumatua Charitable Trust 
                                                   0.0832485440 
                                Raukatauri Music Therapy Centre 
                                                   0.0460472634 
                                  Raukura Hauora O Tainui Trust 
                                                   0.0092424538 
                                       Rayonier New Zealand Ltd 
                                                   0.0258847376 
                              Refugees as Survivors New Zealand 
                                                   0.0568509437 
                                  Reid Construction Systems Ltd 
                                                   0.0186146975 
                                               Renewable Energy 
                                                   0.0039634640 
                                                       Repromed 
                                                   0.1161483663 
                                    Reserve Bank of New Zealand 
                                                   0.0508886384 
                                        Resilient Organisations 
                                                   0.0507825179 
                       Resource Teacher: Learning and Behaviour 
                                                   0.0460472634 
                                          Revolution Fibres Ltd 
                                                   0.0784942708 
                                               Riccarton Rotary 
                                                   0.0000000000 
                        Risk Strategies Research and Consulting 
                                                   0.0074309772 
                                             Rivuli Development 
                                                   0.0089554611 
                                                RML Engineering 
                                                   0.0087353529 
                                         Roche Products Limited 
                                                   0.0568509437 
                                            Rockwell Automation 
                                                   0.0460472634 
                                    Rolleston Veterinary Clinic 
                                                   0.0726522686 
                                  Ropata Village Medical Centre 
                                                   0.0705696678 
                                 Rotorua General Practice Group 
                                                   0.0769323668 
                                       Rowe Davies Research Ltd 
                                                   0.0260816842 
      Royal Australian and New Zealand College of Psychiatrists 
                                                   0.0460472634 
        Royal Forest and Bird Protection Society of New Zealand 
                                                   0.0240634410 
             Royal New Zealand College of General Practitioners 
                                                   0.0678757259 
                              Royal New Zealand Plunket Society 
                                                   0.0534802418 
                                   Royal Society of New Zealand 
                                                   0.0890977766 
                      Ruaimoko Productions and Consultancy Ltd. 
                                                   0.0154425517 
                                                     Rumenz Ltd 
                                                   0.0484310657 
                                                      RuralLink 
                                                   0.0087353529 
 [ reached getOption("max.print") -- omitted 511 entries ]

$value
[1] 21.71682

$options
$options$bmat
[1] "I"

$options$n
[1] 1511

$options$which
[1] "LA"

$options$nev
[1] 1

$options$tol
[1] 0

$options$ncv
[1] 0

$options$ldv
[1] 0

$options$ishift
[1] 1

$options$maxiter
[1] 3000

$options$nb
[1] 1

$options$mode
[1] 1

$options$start
[1] 1

$options$sigma
[1] 0

$options$sigmai
[1] 0

$options$info
[1] 0

$options$iter
[1] 3

$options$nconv
[1] 1

$options$numop
[1] 40

$options$numopb
[1] 0

$options$numreo
[1] 27
top_10_eig2 <- tail(sort(eig2$vector),10)
top_10_eig2
                             NIWA             University of Waikato                    AUT University 
                        0.1576988                         0.1897041                         0.1992335 
 Canterbury District Health Board    Auckland District Health Board Victoria University of Wellington 
                        0.2127479                         0.2346215                         0.2896466 
         University of Canterbury                 Massey University               University of Otago 
                        0.3085040                         0.4043171                         0.6707261 
           University of Auckland 
                        1.0000000 
bottom_10_eig2 <- head(sort(eig2$vector),10)
bottom_10_eig2
                            Alzheimers Northland                                  AP EnerTec Ltd. 
                                               0                                                0 
Aviation Industry Association of New Zealand Inc                            Bio Soil and Crop Ltd 
                                               0                                                0 
                                Blues Rugby Club                    Bruce Shallard and Associates 
                                               0                                                0 
                      ChangeMakers Refugee Forum                      Chatham Rock Phosphate Ltd. 
                                               0                                                0 
                      Chilton Saint James School                     Crown Fibre Holdings Limited 
                                               0                                                0 

Вывод: Минимальные значения центральностей по собственному значению также составляют 0. Наибольшую же имеет университет Окленда. Его высокий показатель говорит, что сам университет связан со многими вершинами, которые в свою очередь имеют также высокое значение центральности.

Выводы

# объединим все центральности в один датафрейм и посмотрим корреляции в двух вариантах 
df1 <- data.frame(deg, clos1, betw1, eig1$vector)
cor(df1)
                    deg       clos1       betw1 eig1.vector
deg          1.00000000 -0.03452649  0.96148582   0.8926645
clos1       -0.03452649  1.00000000 -0.01592647  -0.1091064
betw1        0.96148582 -0.01592647  1.00000000   0.7596773
eig1.vector  0.89266448 -0.10910642  0.75967732   1.0000000
df2 <- data.frame(deg, clos2, betw2, eig2$vector)
cor(df2)
                    deg       clos2       betw2 eig2.vector
deg          1.00000000 -0.03349182  0.90929438   0.8418800
clos2       -0.03349182  1.00000000 -0.01198628  -0.1332681
betw2        0.90929438 -0.01198628  1.00000000   0.7737961
eig2.vector  0.84188004 -0.13326806  0.77379607   1.0000000

Вывод: Составив корреляционные матрицы заметим, что существует высокая корреляция между следующими парами центральностей вершин: по степени - по кратчайшему расстоянию, по степени - по собств. значению и по собств. значению - по кратчайшему расстоянию

Сравним, какие организации попадали в топы по центральностям (исключая центральность по близости).


corr1 <- data.frame(
  names(top_10_degree), 
  names(top_10_betw1), 
  names(top_10_eig1)
)
corr1

corr2 <- data.frame(
  names(top_10_degree), 
  names(top_10_betw2), 
  names(top_10_eig2)
)
corr2

Выводы по Заданию 3: Сравнив топы по максимальным центральностям (за исключением топа центральностей по близости из-за малого количества соседей [порядка 1]), заметим, что по трем центральностям первую пятерку занимают одни и те же организации: университет Окленда, университет Отаго, университет Мэсси, университет Кантербери и Викторианский университет Веллингтона.


Задание 4

В Задании 4 нам предлагается рассчитать ассортативность и гомофилию для графа. Начнем исследование данных с ассортативности:

Ассортативность

# Возникли проблемы с вычислением ассортативности через
# assortativity_nominal(net, types=V(net)$type, directed=F) 
# Предупреждение: в результате преобразования созданы NA
# [1] NaN
assortativity_nominal(net, types=V(net)$type, directed=F)
Предупреждение: в результате преобразования созданы NA
[1] NaN
# Поэтому было принято решение создать новый столбец с закодированными строками

V(net)$num_type <- ifelse( V(net)$type=="Business Enterprise", 1, 
                          ifelse( V(net)$type=="Private not for profit", 2, 
                              ifelse( V(net)$type=="Government", 3, 
                                  ifelse( V(net)$type=="Higher Education", 4, 0) 
                              ) 
                          ) 
                       )
assort_nom <- assortativity_nominal(net, types=V(net)$num_type, directed=F) 
assort_nom # -0.05876298
[1] -0.05876298
# значение ассортативности не зависит от конкретных чисел
V(net)$num_type1 <- ifelse( V(net)$type=="Business Enterprise", 2, 
                           ifelse( V(net)$type=="Private not for profit", 7, 
                               ifelse( V(net)$type=="Government", 5, 
                                  ifelse( V(net)$type=="Higher Education", 10, 0) 
                               ) 
                           ) 
                        )
assortativity_nominal(net, types=V(net)$num_type1, directed=F) # -0.05876298
[1] -0.05876298

Обобщение результатов: Ассортативность в графе по типу вершин примерно равна -0.059. Это означает, что мы не можем утверждать наличие предпочтительного присоединения узлов сети к своему типу (среди узлов в общем, т.е. среди узлов всех типов).

Ассортативность по степени вершины составляет примерно -0.336, что говорит о предпочтительном присоединении узлов к вершинам с относительно небольшим количеством соседей.

Для выявления более точного эффекта предпочтительного присоединения именно среди университетов (что интересует нас в рамках исследовательского вопроса) рассчитаем показатели гомофилии для университетов и других типов институтов.

Нами было принято решение рассчитать dyadicity (ее посчитаем только для одного случая, т.к. она не будет меняться при различных разбиениях) и heterophilicity учреждений высшего образования для следующих разделений на подгруппы: - Higher Education vs все остальные - Higher Education vs Business Enterprise - Higher Education vs Government.

Замечание:

Влиянием Private not for profit можно пренебречь.

Higher Education vs все остальные

p <- edge_density(net)
p # 0.003745601
[1] 0.003745601
n_c <- sum( V(net)$type == 'Higher Education' )
n_c # 54
[1] 54
exp_diad_uni <- n_c * (n_c - 1) / 2 * p
exp_diad_uni # 5.359955
[1] 5.359955
unis <- V(net)[which( V(net)$type == 'Higher Education' )]
unis <- names(unis)
# unis

m_c <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% unis) ) {
    m_c <- m_c + 1
  }
}

m_c # 172
[1] 172
diadicity_uni <- m_c / exp_diad_uni 
diadicity_uni # 32.08982
[1] 32.08982
# 2-й способ посчитать dyadicity
uni_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type == 'Higher Education' )] 
)
# uni_net
# V(uni_net)$type # проверяем, что все вершины в новом графе вузы

edge_density(net) # 0.003745601
[1] 0.003745601
edge_density(uni_net) # 0.1201957
[1] 0.1201957
edge_density(uni_net) / edge_density(net) # 32.08982
[1] 32.08982
n_c # 54
[1] 54
p # 0.003745601
[1] 0.003745601
n_nc <- sum( V(net)$type != 'Higher Education' )
n_nc # 1457
[1] 1457
exp_hetero_uni <- n_nc * n_c * p
exp_hetero_uni # 294.6964
[1] 294.6964
m_mixed <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && !(to_obj %in% unis) ) {
    m_mixed <- m_mixed + 1
  }
  if ( !(from_obj %in% unis) && (to_obj %in% unis) ) {
    m_mixed <- m_mixed + 1
  }
}

m_mixed # 2051
[1] 2051
heterophilicity_uni <- m_mixed / exp_hetero_uni
heterophilicity_uni # 6.959706
[1] 6.959706

Higher Education vs Business Enterprise

# uni_biz_net <- induced_subgraph( 
#   net, 
#   v=V(net)[which( 
#     (V(net)$type == 'Higher Education') || (V(net)$type == 'Business Enterprise') 
#       )] 
# )
uni_biz_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type %in% c('Higher Education', 'Business Enterprise') )] 
)
# uni_biz_net
# V(uni_biz_net)$type

uni_wout_biz_net <- induced_subgraph( 
  uni_biz_net, 
  v=V(uni_biz_net)[which( V(uni_biz_net)$type == 'Higher Education' )] 
)
# uni_wout_biz_net
# V(uni_wout_biz_net)$type


p_uni_vs_biz <- edge_density(uni_biz_net)
p_uni_vs_biz # 0.003036165
[1] 0.003036165
edge_density(uni_wout_biz_net) # 0.1201957
[1] 0.1201957
dyadicity_uni_vs_biz <- edge_density(uni_wout_biz_net) / p_uni_vs_biz 
dyadicity_uni_vs_biz # 39.58799
[1] 39.58799
n_c # 54
[1] 54
p_uni_vs_biz # 0.003036165
[1] 0.003036165
n_nc_biz <- sum( V(net)$type == 'Business Enterprise' )
n_nc_biz # 1010
[1] 1010
exp_hetero_uni_vs_biz <- n_nc_biz * n_c * p_uni_vs_biz
exp_hetero_uni_vs_biz # 165.5925
[1] 165.5925
biz <- V(net)[which( V(net)$type == 'Business Enterprise' )]
biz <- names(biz)
# biz

m_mixed_vs_biz <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% biz) ) {
    m_mixed_vs_biz <- m_mixed_vs_biz + 1
  }
  if ( (from_obj %in% biz) && (to_obj %in% unis) ) {
    m_mixed_vs_biz <- m_mixed_vs_biz + 1
  }
}

m_mixed_vs_biz # 1139
[1] 1139
heterophilicity_uni_vs_biz <- m_mixed_vs_biz / exp_hetero_uni_vs_biz
heterophilicity_uni_vs_biz # 6.878333
[1] 6.878333

Higher Education vs Government

uni_gov_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type %in% c('Higher Education', 'Government') )] 
)
# V(uni_gov_net)$type

uni_wout_gov_net <- induced_subgraph( 
  uni_gov_net, 
  v=V(uni_gov_net)[which( V(uni_gov_net)$type == 'Higher Education' )] 
)
# V(uni_wout_gov_net)$type


p_uni_vs_gov <- edge_density(uni_gov_net) 
p_uni_vs_gov # 0.04231381
[1] 0.04231381
edge_density(uni_wout_gov_net) # 0.1201957
[1] 0.1201957
dyadicity_uni_vs_gov <- edge_density(uni_wout_gov_net) / p_uni_vs_gov 
dyadicity_uni_vs_gov # 2.840578
[1] 2.840578
n_c # 54
[1] 54
p_uni_vs_gov # 0.04231381
[1] 0.04231381
n_nc_gov <- sum( V(net)$type == 'Business Enterprise' )
n_nc_gov # 1010
[1] 1010
exp_hetero_uni_vs_gov <- n_nc_gov * n_c * p_uni_vs_gov
exp_hetero_uni_vs_gov # 2307.795
[1] 2307.795
gov <- V(net)[which( V(net)$type == 'Business Enterprise' )]
gov <- names(gov)
# gov

m_mixed_vs_gov <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% gov) ) {
    m_mixed_vs_gov <- m_mixed_vs_gov + 1
  }
  if ( (from_obj %in% gov) && (to_obj %in% unis) ) {
    m_mixed_vs_gov <- m_mixed_vs_gov + 1
  }
}

m_mixed_vs_gov # 0.4935447
[1] 1139
heterophilicity_uni_vs_gov <- m_mixed_vs_gov / exp_hetero_uni_vs_gov
heterophilicity_uni_vs_gov # 0.4935447
[1] 0.4935447

Соберем полученные значения dyadicity и heterophilicity вместе: - Higher Education vs все остальные: - dyadicity: 32.0898241 - heterophilicity: 6.9597056 - Higher Education vs Business Enterprise: - dyadicity: 39.5879866 - heterophilicity: 6.8783329 - Higher Education vs Government: - dyadicity: 2.840578 - heterophilicity: 0.4935447.

Мы видим, что dyadicity университетов при разделении на университеты и всех остальных (а также при разделении на университеты и бизнес) очень высокая. При этом heterophilicity также доволльно сильно превышает 1.

В чем может быть объяснение этой особенности данных? Как утверждается в статье “Functional dyadicity and heterophilicity of gene-gene interactions in statistical epistasis networks”, описанный выше факт может быть связан с тем, что вершины со значением метки 1 имеют большую центральность \(\Rightarrow\) хорошо связаны друг с другом и с вершинами другого типа.

В Задании 6 мы будем проверять гипотезу касательно высоких степеней вершин типа Higher Education среди крупных университетов.

Выводы

Выводы по Заданию 4: Мы получили, что несмотря на плотные связи учреждений высшего образования между собой, по крайней мере некоторые из них имеют также прочные связи с другими типами организаций (в частности с бизнесом).


Задание 5

Проведем процедуру кластеризации вершин при помощи Edge-betweenness и Fast-greedy методов и сравним полученные результаты с существующей классификацией.

Т.к. считать кратчайший путь для исходных весов ребер является не очень осмысленным, используем обратные для исходных веса ребер.

Замечание: Для Fast-greedy не важно, какие данные использовать: исходные или инвертированные, т.к. этот метод не учитывает веса ребер (только их количество).

# проводим кластеризацию при помощи метода Edge-betweenness
ceb <- cluster_edge_betweenness(net, weights=E(net)$weight)
Предупреждение: At core/community/edge_betweenness.c:493 : Membership vector will be selected based on the highest modularity score.
# смотрим на полученные в результате кластеризации объекты
mbship_ceb <- membership(ceb) 
# mbship_ceb

s_ceb <- sizes(ceb)
s_ceb
Community sizes
  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26 
 45 213 233 154 229 190  75  46 164  48  32   2   2   2   3  15   2   2   8   2   2   4   2   2   2   2 
 27  28  29  30  31  32  33  34  35  36  37  38 
  7   2   2   2   2   2   2   2   2   2   3   2 
ms_ceb <- modularity(ceb)
ms_ceb # 0.527262
[1] 0.527262
# ceb
# > s_ceb <- sizes(ceb)
# > s_ceb
# Community sizes
#   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
#  45 213 233 154 229 190  75  46 164  48  32   2   2   2   3  15   2   2   8   2 
#  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38 
#   2   4   2   2   2   2   7   2   2   2   2   2   2   2   2   2   3   2 
# > ms_ceb <- modularity(ceb)
# > ms_ceb
# [1] 0.527262

Визуализация кластеризации методом Edge-betweenness:

plot(
  ceb, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_nicely
)

plot(
  ceb, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_with_lgl
)

Сравним результаты кластеризации Edge-betweenness и имеющуюся классификацию вершин:

compare(ceb, V(net)$type, method='nmi') # 
[1] 0.03399001
# здесь и далее мы используем нормализованное значение функции compare() для облегчения интерпретации возвращаемого результата

Таким образом, мы видим, что имеющаяся классификация вершин совсем не похожа на то, что мы получили при кластеризации. По всей видимости, “разделение по бутылочному горлышку” является не очень хорошим способом для кластеризации вершин в нашем датасете.

# проводим кластеризацию при помощи метода Fast-greedy
cfg <- cluster_fast_greedy(net, weights=E(net)$weight) 

# смотрим на полученные в результате кластеризации объекты
mbship_cfg <- membership(cfg) 
# mbship_cfg

s_cfg <- sizes(cfg)
s_cfg
Community sizes
  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26 
219 144 212 132 141  94 189 120  84  82  28   3   2  15   3   3   2   2   2   2   2   2   2   2   2   2 
 27  28  29  30  31  32  33  34  35  36 
  2   2   2   2   2   2   2   2   2   2 
ms_cfg <- modularity(cfg)
ms_cfg # 0.5310055
[1] 0.5310055
# cfg
# > s_cfg <- sizes(cfg)
# > s_cfg
# Community sizes
#   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26 
# 219 144 212 132 141  94 189 120  84  82  28   3   2  15   3   3   2   2   2   2   2   2   2   2   2   2 
#  27  28  29  30  31  32  33  34  35  36 
#   2   2   2   2   2   2   2   2   2   2 
# > ms_cfg <- modularity(cfg)
# > ms_cfg
# [1] 0.5310055

Визуализация кластеризации методом Fast-greedy:

plot(
  cfg, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_nicely
)

plot(
  cfg, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_with_lgl
)

compare(cfg, V(net)$type, method='nmi') # 0.03386511
[1] 0.03386511

Таким образом, мы видим, что так же, как и предыдущий способ кластеризации, Fast-greedy не очень хорошо соответствует реальной классификации рассматриваемых институтов.

Выводы

Вывод по Заданию 5: Известные нам способы кластеризации (Edge-betweenness и Fast-greedy) не дали результата, похожего на имеющуюся в датасете классификацию.


Задание 6

Изначально был поставлен исследовательский вопрос, насколько активно при написании научных работ университеты Новой Зеландии взаимодействуют с другими типами организаций, нужно ли им как-то в этом способстовать извне (например, создавать общие лаботарии с индустриальными корпорациями и государственными органами). Помимо расчета значений гомофилии и различных видов центральностей, для ответа на заданный вопрос нам может помочь модель предсказания класса вершин Relational Neighbors Classifier (RNC).

Разделим все вершины на 2 класса: “1” - университет, “0” - иначе. Отберем из каждого класса по 10 вершин и положим вероятности их принадлежности первому классу соответственно 1 и 0. Для всех остальных вершин (unknown) положим эту вероятность равной 0.5. При каждой итерации будем обновлять вероятности каждой вершины исходя из вероятностей её соседей. В итоге, после 10 таких итераций получим для каждой вершины вероятность её принадлежности классу “1”, и отберем те вершины, чья вероятность больше порога 0.5 в качестве принадлежащих классу “1”.

Для избежания случайности повторим этот алгоритм 100 раз и построим гистограмму распределения числа предсказанных университетов, а также гистограмму распределения средних вероятностей принадлежности группе университетов.

res <- rep(NA, 20)
pr <- rep(NA, 20)

for (j in 1:20){ 
  network <- net
  V(network)[which( V(network)$type == 'Higher Education' )]$type = 1
  V(network)[which(V(network)$type != 1)]$type = 0
  
  
  # вероятность вершины перейти в класс churn = 1 равна доле соседей churn = 1 от общего числа соседей
  # используем матричные вычисления
  random_uni <- sample( V(network)[ which(V(network)$type == 1) ], 10 )
  random_not_uni <- sample( V(network)[ which(V(network)$type == 0) ], 10 )
  
  
  for (i in 1:1511){
    if (!(V(network)[i] %in% random_uni | (V(network)[i] %in% random_not_uni))){
      V(network)$type[i] = 0.5
    }
  }
  
  UniProb <-  as.numeric(V(network)$type)
  threshold <- 0.5
  A <- as_adjacency_matrix(network)
  A <- as.matrix(A)
  Neighbors <- rowSums(A) # общее число соседей вершины
  
  UniProb_iter <- UniProb
  for(i in 1:10){
    UniProb_iter <- as.vector((A %*% UniProb_iter) / Neighbors)
  }
  res[j] <- length(which(UniProb_iter > threshold))
  pr[j] <- mean(UniProb_iter)
}
hist(res, main='Число предсказанных университетов')

hist(pr, main='Средняя вероятность принадлежности классу 1')

Как можно увидеть, почти во всех случаях абсолютное число вершин предсказанj в качестве университетов. Получаем, что какие бы 10 университетов мы ни взяли, их класс дойдет до большинства вершин быстрее, чем противоположный класс 10 случайных вершин. Это распространяется и на случай, когда были выбраны наименее центральные университеты. Если бы университеты были плохо связаны с организациями другого типа, то их класс намного слабее распространялся бы на вершины другого типа, а это не так.

Значит, по крайней мере какие-то университеты (а именно наиболее центральные) довольно активно кооперируются с другими организациями (как, например, это делает Оклендский университет). Поэтому для таких университетов нет необходимости строить совместные с бизнесом и государством научные центры.

Вспомним про высокий показатель dyadicity у ВУЗов: выходит, что он получается таким большим из-за высокой гомофилии более мелких учебных заведений. Тогда можно предположить, что именно они плохо взаимодействуют с бизнесом и гос. органами.


Заключение

Как тогда можно им помочь? При моделировании их класс распространялся по сети через их соседей — крупные университеты. В таком случае, более разумно строить научные центры именно соединяющие мелкие университеты с крупными. Данным образом, казалось бы, усиливая гомофилию, мы, наоборот, будем способстовать развитию научных отношений университетов с индустриальными партнерами.

Замечание

Здесь мы предполагаем эталонность крупных университетов (например, Оклендского) с точки зрения эффективности взаимодействия, а также качества и количества научных работ, что продемонстрировано, например, в этой статье.

---
title: "Дз по Сетевым моделям"
output:
  pdf_document: default
  author: "Кабанов Илья, Сухов Александр, Сысоев Никита"
  html_notebook: default
---

## Подготовительные шаги

```{r}
# Установим рабочую директорию
setwd("~/Documents/GitHub/RProjects_EF/Networks")
```

```{r}
# Подгрузим необходимые для дальнейшего анализа библиотеки
## install.packages("igraph")
## install.packages("igraphdata")
## install.packages("ggraph")
## install.packages("tidygraph")
## install.packages("DescTools")


library(igraph);
library(igraphdata);
library(ggraph);
library(tidygraph);
library(DescTools);
```

## Обработка данных и создание графа

```{r}
# Загрузим данные для исследования: набор ребер и вершин
edges <- read.csv("edges_1.csv", header=T) 
colnames(edges) <- c('from', 'to', 'type1', 'type2', 'weight')

nodes <- unique(edges[c('from', 'type1')])
more_nodes <- unique(edges[c('to', 'type2')])

colnames(nodes) <- c('organisation', 'type')
colnames(more_nodes) <- c('organisation', 'type')

nodes <- rbind(nodes, more_nodes)
nodes <- unique(nodes[c('organisation', 'type')])
rownames(nodes) <- NULL
edges <- edges[c('from', 'to', 'weight')]

# Создадим также набор обратных величин для весов ребер (это пригодится нам в дальнейшем). Исходные веса нам уже не понадобятся
edges$weight <- 1 / edges$weight

net <- graph_from_data_frame(d=edges, vertices=nodes, directed=F)

V(net)$color <- ifelse( V(net)$type=="Business Enterprise", "red", 
  ifelse( V(net)$type=="Private not for profit", "purple", 
    ifelse( V(net)$type=="Government", "green", 
      ifelse( V(net)$type=="Higher Education", "blue", "black") 
    ) 
  ) 
)
head(V(net)$color, 10)
```

**Поясним, почему в дальнейшем будем работать именно с обратными весами:** Кратчайший путь и кратчайшее расстояние в данной задаче будут представлять собой не то же самое, что и в задаче с издержками перевозок или длинами расстояний между вершинами в качестве весов ребер. Отрицательные веса мы не используем, потому что *алгоритм Дейкстры* работает с неотрицательными весами ребер, поэтому далее мы оперируем с обратными весами, т.к., на наш взгляд, этот выбор является наиболее оптимальным для преодоления возникших трудностей.

------------------------------------------------------------------------

## Исследовательский вопрос

**Исследовательский вопрос:** Какие есть способы улучшения взаимодействия учреждений высшего образования Новой Зеландии (если это вообще требуется)?

Наше исследование показывает, что возможно повысить эффективность небольших университетов посредством увеличения сотрудничества с крупными, которые в свою очередь имеют тесное сотредничество с бизнесом.

Детали см. в *Задании 6*.

------------------------------------------------------------------------

## Анализ датасета

### Описание датасета

Датасет представляет из себя множество вершин с качественными характеристиками и множество ребер с числовыми характеристиками (весами).

Вершинами являются организации Новой Зеландии, которые занимаются написанием научных статей в качестве одного из видов деятельности. Качественной характеристикой вершин является вид организации (государственная организации, высшее учебное заведение, коммерческое предприятие и частное некоммерческое предприятие). Всего в датасете 1511 вершин.

Между `i`-ой и `j`-ой вершинами (организациями) существует ребро, если за период 2010-2015 гг. на Scopus была опубликована хотя бы одна статья, хотя бы один автор которой числится в организации `i`, а другой автор -- в организации `j`. Всего в датасете 4273 ребра.

Вес ребра равен количеству совместных опубликованных научных работ. Если вес ребра между `i`-ой и `j`-ой вершиной равен 3, то это означает, что за указанный период на Scopus было опубликовано 3 научные работы, у которых хотя бы один автор числится в организации `i`, а другой --- в организации `j`.

------------------------------------------------------------------------

### Задание 2

При использовании нескольких пакетов для работы с графами не оказалось возможным интерпретируемо визуализировать граф полностью. Поэтому для отображения структуры нашей сети найдем 100 самых центральных по степени вершин и представим связи между ними при помощи пакета `ggraph`.

```{r}
V(net)$degrees <- degree(net)
nodes$degrees <- V(net)$degrees

for_vis_n <- nodes[order(-nodes$degrees),][1:100, 1:2]
for_vis_e <- edges[(edges$from %in% for_vis_n$organisation & edges$to %in% for_vis_n$organisation),]

for_vis_net <- graph_from_data_frame(d=for_vis_e, vertices=for_vis_n, directed=F)
V(for_vis_net)$degrees <- degree(for_vis_net)

for_vis_net %>%
  ggraph(layout='graphopt') +
  geom_node_point(aes(color = type, size=round(degrees/20))) +
  geom_edge_link(alpha = 0.05) +
  theme_void() +
  ggtitle("Network of New Zealand organisations")
```

Как можно увидеть, среди 100 самых центральных вершин с количественной точки зрения преобладают организации государственного сектора, однако самыми крупными здесь являются новозеландские университеты. Первые 5 мест по числу совместных научных работ принадлежат именно им, лидером по данному показателю является *Университет Окленда*, самый крупный и престижный университет Новой Зеландии.

Рассчитаем **базовые параметры** нашего графа. Так как весами дуг в данном случае является число совместных работ, то есть "сила связи" двух вершин, будем использовать обратные веса для подсчета центральностей через кратчайшие пути. Это довольно разумно, так как от написания дополнительной общей работы прирост в силе связи двух организаций должен монотонно снижаться, как и разница в пути до соседа.

```{r}
#Считаем базовые параметры графа

# Density
# The proportion of present edges from all possible ties.
p <- edge_density(net)

# связность сети
no <- igraph::components(net)$no # в пакете statnet такое же название
csize <- igraph::components(net)$csize
csize


# Diameter (longest geodesic distance) (если несколько компонент, то диаметр самой большой)
# Note that edge weights are used by default, unless set to NA.
diam <- diameter(net, weights=NA)
diam_w <- diameter(net)
path <- get_diameter(net, weights=NA)
path_w <- get_diameter(net)
path
path_w

# рассчитаем кратчайшие пути
# Average path length 
# The mean of the shortest distance between each pair of nodes in the network 
# (in both directions for directed graphs). 
m_dist <- mean_distance(net, weights=NA)
m_dist_w <- mean_distance(net)
```

Плотность нашего графа составляет `r round(p, 4)`. Такая низкая плотность (вероятность образования связи) довольно естественная для вероятности написания научной работы. Наша сеть имеет `r no` компонент связности: одна главная, соединяющая практически все вершины, а все остальные имеют по 2-3 вершины. Диаметр (наибольший из кратчаших путей) имеет длину `r round(diam_w, 2)`, или `r diam`, если брать единичные веса для всех дуг.

**Изучим соседство самой центральной вершины --- Оклендского Университета** (с кем чаще всего взаимодействует наиболее престижный ВУЗ страны):

```{r}
# We can also easily identify the immediate neighbors of a vertex.
# The 'neighbors' function finds all nodes one step out from the focal actor.
# To find the neighbors for multiple nodes, use 'adjacent_vertices()'.
d <- data.frame(neighbors(net, V(net)["University of Auckland"], mode="total")$type)
groups <- as.data.frame(table(d))[, 2]
pie(groups, labels=paste0(as.data.frame(table(d))[, 1], ', ',round(groups/sum(groups)*100, digits=1), '%'), 
    col=c(5, 2, 3, 4), main='Neighbors of University of Auckland')

```

```{r}
# To find node neighborhoods going more than one step out, use function 'ego()'
# with parameter 'order' set to the number of steps out to go from the focal node(s).
neigh2 <- data.frame(ego(net, order = 2, nodes = V(net)["University of Auckland"])[[1]]$type)
groups2 <- as.data.frame(table(neigh2))[, 2]
pie(groups2, labels=paste0(as.data.frame(table(neigh2))[, 1], ', ',round(groups2/sum(groups2)*100, digits=1), '%'), 
    col=c(5, 2, 3, 4), main='Two-step neighbors of University of Auckland')
```

Довольно ожидаемо, что чаще всего в написании научных работ такой успешный университет сотрудничает с индустрией. **Это подтвеждает наше предположение о том, успех научной работы зависит от работы с бизнесом.** В ближайшем окружении данной организации также принято вести исследования с индустрией.

**Сравним нашу сеть с теоритическими моделями случайного графа** на основе *распределения числа их соседей*, *диаметра*, с*реднего кратчайшего пути* и *числа компонент связности*. Начнем с модели случайного графа *Эрдеша-Реньи*.

```{r}
#Генерируем модели случайного графа erdos.renyi
p <- edge_density(net)

random_model <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
```

Как можно заметить, **все рассматриваемые показатели нашей сети значимо отличаются от модельных**, значит, структуру нашей сети нельзя описать данным образом.

**Обратимся к модели "Малого мира"** с регулярной решеткой. Однако в этом случае сперва нужно подобрать гиперпараметр --- долю переприсоединенных дуг.

```{r}
#Генерируем модели случайного графа с регулярной решеткой
n_of_nei <- mean(degree(net))
diam_net <- diameter(net, weights=NA)
#Ищем оптимальное значение p
mean_dist_net <- mean_distance(net)
model <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
res <- rep(NA, 100)
for (i in 1:100){
  model[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = i/100)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

# p = 0.99

random_model <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
```

```{r}
# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
  model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

plot(x=c(1:40)/10, y=res)
#power=2.15

random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
```

**Аналогично предыдущему случаю, данная модель плохо описывает структуру нашего графа.** Значимо совпадает лишь диаметр, так как по нему в том числе происходил подбор гиперпараметра.

Рассмотрим также **схожесть с моделью Барабаши-Альберта**, включающей предпочтительное присоединение к наиболее центральным вершинам.

```{r}

# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
  model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

#power=2.15

random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)

```

Как мы получили, данная модель тоже не подходит для описания структуры новозеландской сети: все статистически значимо отличается, кроме параметра, по которому проходил подбор гиперпараметра.

#### Выводы

**Выводы по *Заданию 2*:** Ни одна из теоретических моделей, известных нам, не описывает структуры нашего графа достаточно точно.

------------------------------------------------------------------------

### Задание 3

В этом задании нам предлагается посчитать различные меры *центральности вершин* и сделать содержательные выводы на основе полученных расчетов.

Замечание

:   Для анализа используем обратные веса, т.к. их использование делает осмысленным расчет центральности по близости и кратчайшему пути, но не искажает остальных мер центральности вершин.

#### Центральность по степени

Для начала посчитаем **центральность по степени**:

```{r}
deg <- degree(net)

# plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=deg)
```

Теперь построим *гистограмму распределения степеней вершин*:

```{r}
# гистограмма степеней вершин
hist(deg, main="Histogram of node degree", breaks=50, prob=TRUE) 
# распределение степеней вершин

mean(deg) # Средняя степень вершины по графу
# ~ 5.66
Mode(deg) # Модальная степень вершин графа
# 1 -> 599 раз
median(deg) # Медиана степеней вершин
# ~ 2
top_10_degree <- tail(sort(deg), 10) # топ-10 по степеням
top_10_degree # в топе - 7 университетов, 3 гос. учреждения
```

**Вывод:** Центральность вершин по степени не зависит от весов. Подавляющее большинство вершин имеет степень, меньшую `50`. Так, медиана кол-ва соседей равняется `r round(median(deg))`. В среднем у вершины такого графа степень равна `r round(mean(deg), 2)`. Наиболее часто встречающаяся степень вершины --- 1, которая встречается 599 раз. Если мы посмотрим 10 вершин с наибольшим числом соседей, то окажется, что 7 из них являются университетами, в числе которых крупнейший --- университет Окленда (степень вершины максимальная --- `r max(deg)`). Оставшиеся 3 организации являются государственными: 2 департамента здравоохранения и 1 исследовательская компания. Степень у всех вершин, входящих в топ-10, \> 100.

#### Центральность по близости

Далее рассчитаем **центральность по близости** двумя способами: В первом варианте все веса ребер графа являются `1`, в другом используются обратные веса ребер.

```{r}
clos1 <- closeness(net, weights=NA) # Первый способ - без учета весов
clos1

plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos1 * 50)
```

```{r}
top_10_clos1 <- tail(sort(clos1), 10) 
# Вектор-топ 42 также будет единичным, а вот вектор-топ 43 уже нет
top_10_clos1

bottom_10_clos1 <- head(sort(clos1), 10)
bottom_10_clos1

clos1["University of Auckland"]
```

```{r}
clos2 <- closeness(net)
clos2

plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos2 * 50)
```

```{r}
top_10_clos2 <- tail(sort(clos2), 10) 
top_10_clos2

bottom_10_clos2 <- head(sort(clos2), 10)
bottom_10_clos2

clos2["University of Auckland"]
```

**Вывод:** В обоих случаях максимальная центральность вершин будет составлять `1`. В нашем графе существует 21 пара вершин, которая связана лишь между собой и более ни с кем (из рассчета для графа с единичными весами ребер). Из них лишь 5 организаций работали совместно более 1 раза (из рассчета для графа с обратными весами). Топ-10 центральных вершин по близости и топ-10 по степени уже существенно различаются. Так, центральность по близости университета Окленда составит `r clos1["University of Auckland"]` в первом случае и `r clos1["University of Auckland"]`. Т.е. `round(1 / clos1["University of Auckland"])` или `round(1 / clos2["University of Auckland"])` --- сумма длин всех путей от университета Окленда до любой другой вершины в зависимости от метода рассчета.

#### Центральность по кратчайшему пути

```{r}
betw1 <- betweenness(net, weights=NA)
head(betw1)

top_10_betw1 <- tail(sort(betw1), 10)
top_10_betw1

bottom_10_betw1 <- head(sort(betw1), 10)
bottom_10_betw1

betw1["University of Auckland"]
```

```{r}
betw2 <- betweenness(net)
head(betw2)

top_10_betw2 <- tail(sort(betw2), 10)
top_10_betw2

bottom_10_betw2 <- head(sort(betw2), 10)
bottom_10_betw2

betw2["University of Auckland"]
```

**Вывод:** При разных методах минимальные значения центральности у вершин будут равны `0`. Это вершины, расположенные на периферии графа, или те, которые вовсе имеют всего одного соседа (например, та 21 пара вершин). Максимальные центральности вершин превышают `40 000` в топ-10. В обоих случаях университет Окленда на первом месте (`r max(betw1)` и `r max(betw2)`). Значительное число кратчайших путей между любыми двумя вершинами проходит именно через данный университет.

#### Центральность по собственному значению

```{r}
eig1 <- eigen_centrality(net, weights = NA)
head(eig1)

top_10_eig1 <- tail(sort(eig1$vector), 10)
top_10_eig1

bottom_10_eig1 <- head(sort(eig1$vector), 10)
bottom_10_eig1
```

```{r}
eig2 <- eigen_centrality(net)
head(eig2)

top_10_eig2 <- tail(sort(eig2$vector),10)
top_10_eig2

bottom_10_eig2 <- head(sort(eig2$vector),10)
bottom_10_eig2
```

**Вывод:** Минимальные значения центральностей по собственному значению также составляют `0`. Наибольшую же имеет университет Окленда. Его высокий показатель говорит, что сам университет связан со многими вершинами, которые в свою очередь имеют также высокое значение центральности.

#### Выводы

```{r}
# объединим все центральности в один датафрейм и посмотрим корреляции в двух вариантах 
df1 <- data.frame(deg, clos1, betw1, eig1$vector)
cor(df1)

df2 <- data.frame(deg, clos2, betw2, eig2$vector)
cor(df2)
```

**Вывод:** Составив корреляционные матрицы заметим, что существует высокая корреляция между следующими парами центральностей вершин: по степени - по кратчайшему расстоянию, по степени - по собств. значению и по собств. значению - по кратчайшему расстоянию

Сравним, какие организации попадали в топы по центральностям (исключая центральность по близости).

```{r}

corr1 <- data.frame(
  names(top_10_degree), 
  names(top_10_betw1), 
  names(top_10_eig1)
)
corr1

corr2 <- data.frame(
  names(top_10_degree), 
  names(top_10_betw2), 
  names(top_10_eig2)
)
corr2
```

**Выводы по Заданию 3:** Сравнив топы по максимальным центральностям (за исключением топа центральностей по близости из-за малого количества соседей [порядка 1]), заметим, что по трем центральностям первую пятерку занимают одни и те же организации: университет Окленда, университет Отаго, университет Мэсси, университет Кантербери и Викторианский университет Веллингтона.

------------------------------------------------------------------------

### Задание 4

В *Задании 4* нам предлагается рассчитать *ассортативность* и *гомофилию* для графа. Начнем исследование данных с *ассортативности*:

#### Ассортативность

```{r}
# Возникли проблемы с вычислением ассортативности через
# assortativity_nominal(net, types=V(net)$type, directed=F) 
# Предупреждение: в результате преобразования созданы NA
# [1] NaN
assortativity_nominal(net, types=V(net)$type, directed=F)
```

```{r}
# Поэтому было принято решение создать новый столбец с закодированными строками

V(net)$num_type <- ifelse( V(net)$type=="Business Enterprise", 1, 
                          ifelse( V(net)$type=="Private not for profit", 2, 
                              ifelse( V(net)$type=="Government", 3, 
                                  ifelse( V(net)$type=="Higher Education", 4, 0) 
                              ) 
                          ) 
                       )
```

```{r}
assort_nom <- assortativity_nominal(net, types=V(net)$num_type, directed=F) 
assort_nom # -0.05876298
```

```{r}
# значение ассортативности не зависит от конкретных чисел
V(net)$num_type1 <- ifelse( V(net)$type=="Business Enterprise", 2, 
                           ifelse( V(net)$type=="Private not for profit", 7, 
                               ifelse( V(net)$type=="Government", 5, 
                                  ifelse( V(net)$type=="Higher Education", 10, 0) 
                               ) 
                           ) 
                        )
```

```{r}
assortativity_nominal(net, types=V(net)$num_type1, directed=F) # -0.05876298
```

```{r}
# считаем ассортативность по степени вершины
assort_deg <- assortativity_degree(net, directed=F) # -0.3361749
assort_deg
```

**Обобщение результатов:** *Ассортативность* в графе по типу вершин примерно равна `r round(assort_nom, 3)`. Это означает, что мы не можем утверждать наличие предпочтительного присоединения узлов сети к своему типу (среди узлов в общем, т.е. среди узлов всех типов).

*Ассортативность* по степени вершины составляет примерно `r round(assort_deg, 3)`, что говорит о предпочтительном присоединении узлов к вершинам с относительно небольшим количеством соседей.

> Для выявления более точного эффекта предпочтительного присоединения именно среди университетов (что интересует нас в рамках исследовательского вопроса) рассчитаем показатели гомофилии для университетов и других типов институтов.

Нами было принято решение рассчитать *dyadicity* (ее посчитаем только для одного случая, т.к. она не будет меняться при различных разбиениях) и *heterophilicity* учреждений высшего образования для следующих разделений на подгруппы: - `Higher Education` vs все остальные - `Higher Education` vs `Business Enterprise` - `Higher Education` vs `Government`.

<ins>Замечание:</ins>

Влиянием `Private not for profit` можно пренебречь.

#### `Higher Education` vs все остальные

```{r}
p <- edge_density(net)
p # 0.003745601
n_c <- sum( V(net)$type == 'Higher Education' )
n_c # 54
exp_diad_uni <- n_c * (n_c - 1) / 2 * p
exp_diad_uni # 5.359955

unis <- V(net)[which( V(net)$type == 'Higher Education' )]
unis <- names(unis)
# unis

m_c <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% unis) ) {
    m_c <- m_c + 1
  }
}

m_c # 172

diadicity_uni <- m_c / exp_diad_uni 
diadicity_uni # 32.08982
```

```{r}
# 2-й способ посчитать dyadicity
uni_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type == 'Higher Education' )] 
)
# uni_net
# V(uni_net)$type # проверяем, что все вершины в новом графе вузы

edge_density(net) # 0.003745601
edge_density(uni_net) # 0.1201957

edge_density(uni_net) / edge_density(net) # 32.08982
```

```{r}
n_c # 54
p # 0.003745601
n_nc <- sum( V(net)$type != 'Higher Education' )
n_nc # 1457

exp_hetero_uni <- n_nc * n_c * p
exp_hetero_uni # 294.6964

m_mixed <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && !(to_obj %in% unis) ) {
    m_mixed <- m_mixed + 1
  }
  if ( !(from_obj %in% unis) && (to_obj %in% unis) ) {
    m_mixed <- m_mixed + 1
  }
}

m_mixed # 2051

heterophilicity_uni <- m_mixed / exp_hetero_uni
heterophilicity_uni # 6.959706
```

#### `Higher Education` vs `Business Enterprise`

```{r}
# uni_biz_net <- induced_subgraph( 
#   net, 
#   v=V(net)[which( 
#     (V(net)$type == 'Higher Education') || (V(net)$type == 'Business Enterprise') 
#       )] 
# )
uni_biz_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type %in% c('Higher Education', 'Business Enterprise') )] 
)
# uni_biz_net
# V(uni_biz_net)$type

uni_wout_biz_net <- induced_subgraph( 
  uni_biz_net, 
  v=V(uni_biz_net)[which( V(uni_biz_net)$type == 'Higher Education' )] 
)
# uni_wout_biz_net
# V(uni_wout_biz_net)$type


p_uni_vs_biz <- edge_density(uni_biz_net)
p_uni_vs_biz # 0.003036165
edge_density(uni_wout_biz_net) # 0.1201957

dyadicity_uni_vs_biz <- edge_density(uni_wout_biz_net) / p_uni_vs_biz 
dyadicity_uni_vs_biz # 39.58799
```

```{r}
n_c # 54
p_uni_vs_biz # 0.003036165
n_nc_biz <- sum( V(net)$type == 'Business Enterprise' )
n_nc_biz # 1010

exp_hetero_uni_vs_biz <- n_nc_biz * n_c * p_uni_vs_biz
exp_hetero_uni_vs_biz # 165.5925

biz <- V(net)[which( V(net)$type == 'Business Enterprise' )]
biz <- names(biz)
# biz

m_mixed_vs_biz <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% biz) ) {
    m_mixed_vs_biz <- m_mixed_vs_biz + 1
  }
  if ( (from_obj %in% biz) && (to_obj %in% unis) ) {
    m_mixed_vs_biz <- m_mixed_vs_biz + 1
  }
}

m_mixed_vs_biz # 1139

heterophilicity_uni_vs_biz <- m_mixed_vs_biz / exp_hetero_uni_vs_biz
heterophilicity_uni_vs_biz # 6.878333
```

#### `Higher Education` vs `Government`

```{r}
uni_gov_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type %in% c('Higher Education', 'Government') )] 
)
# V(uni_gov_net)$type

uni_wout_gov_net <- induced_subgraph( 
  uni_gov_net, 
  v=V(uni_gov_net)[which( V(uni_gov_net)$type == 'Higher Education' )] 
)
# V(uni_wout_gov_net)$type


p_uni_vs_gov <- edge_density(uni_gov_net) 
p_uni_vs_gov # 0.04231381
edge_density(uni_wout_gov_net) # 0.1201957

dyadicity_uni_vs_gov <- edge_density(uni_wout_gov_net) / p_uni_vs_gov 
dyadicity_uni_vs_gov # 2.840578
```

```{r}
n_c # 54
p_uni_vs_gov # 0.04231381
n_nc_gov <- sum( V(net)$type == 'Business Enterprise' )
n_nc_gov # 1010

exp_hetero_uni_vs_gov <- n_nc_gov * n_c * p_uni_vs_gov
exp_hetero_uni_vs_gov # 2307.795

gov <- V(net)[which( V(net)$type == 'Business Enterprise' )]
gov <- names(gov)
# gov

m_mixed_vs_gov <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% gov) ) {
    m_mixed_vs_gov <- m_mixed_vs_gov + 1
  }
  if ( (from_obj %in% gov) && (to_obj %in% unis) ) {
    m_mixed_vs_gov <- m_mixed_vs_gov + 1
  }
}

m_mixed_vs_gov # 0.4935447

heterophilicity_uni_vs_gov <- m_mixed_vs_gov / exp_hetero_uni_vs_gov
heterophilicity_uni_vs_gov # 0.4935447
```

Соберем полученные значения *dyadicity* и *heterophilicity* вместе: - `Higher Education` vs все остальные: - dyadicity: `r diadicity_uni # 32.08982` - heterophilicity: `r heterophilicity_uni # 6.959706` - `Higher Education` vs `Business Enterprise`: - dyadicity: `r dyadicity_uni_vs_biz # 39.58799` - heterophilicity: `r heterophilicity_uni_vs_biz # 6.878333` - `Higher Education` vs `Government`: - dyadicity: `r dyadicity_uni_vs_gov # 2.840578` - heterophilicity: `r heterophilicity_uni_vs_gov # 0.4935447`.

Мы видим, что dyadicity университетов при разделении на университеты и всех остальных (а также при разделении на университеты и бизнес) очень высокая. При этом heterophilicity также доволльно сильно превышает 1.

В чем может быть объяснение этой особенности данных? Как утверждается в статье ["Functional dyadicity and heterophilicity of gene-gene interactions in statistical epistasis networks"](https://biodatamining.biomedcentral.com/articles/10.1186/s13040-015-0062-4), описанный выше факт может быть связан с тем, что вершины со значением метки `1` имеют большую центральность $\Rightarrow$ хорошо связаны друг с другом и с вершинами другого типа.

В *Задании 6* мы будем проверять гипотезу касательно высоких степеней вершин типа `Higher Education` среди крупных университетов.

#### Выводы

**Выводы по Заданию 4:** Мы получили, что несмотря на плотные связи учреждений высшего образования между собой, по крайней мере некоторые из них имеют также прочные связи с другими типами организаций (в частности с бизнесом).

------------------------------------------------------------------------

### Задание 5

Проведем процедуру кластеризации вершин при помощи Edge-betweenness и Fast-greedy методов и сравним полученные результаты с существующей классификацией.

Т.к. считать кратчайший путь для исходных весов ребер является не очень осмысленным, используем обратные для исходных веса ребер.

Замечание: Для Fast-greedy не важно, какие данные использовать: исходные или инвертированные, т.к. этот метод не учитывает веса ребер (только их количество).

```{r}
# проводим кластеризацию при помощи метода Edge-betweenness
ceb <- cluster_edge_betweenness(net, weights=E(net)$weight)

# смотрим на полученные в результате кластеризации объекты
mbship_ceb <- membership(ceb) 
# mbship_ceb

s_ceb <- sizes(ceb)
s_ceb

ms_ceb <- modularity(ceb)
ms_ceb # 0.527262
```

```{r}
# ceb
```

```{r}
# > s_ceb <- sizes(ceb)
# > s_ceb
# Community sizes
#   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
#  45 213 233 154 229 190  75  46 164  48  32   2   2   2   3  15   2   2   8   2 
#  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38 
#   2   4   2   2   2   2   7   2   2   2   2   2   2   2   2   2   3   2 
```

```{r}
# > ms_ceb <- modularity(ceb)
# > ms_ceb
# [1] 0.527262
```

**Визуализация кластеризации методом Edge-betweenness:**

```{r}
plot(
  ceb, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_nicely
)
```

```{r}
plot(
  ceb, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_with_lgl
)
```

**Сравним результаты кластеризации Edge-betweenness и имеющуюся классификацию вершин:**

```{r}
compare(ceb, V(net)$type, method='nmi') # 
# здесь и далее мы используем нормализованное значение функции compare() для облегчения интерпретации возвращаемого результата
```

Таким образом, мы видим, что имеющаяся классификация вершин совсем не похожа на то, что мы получили при кластеризации. <mark> По всей видимости, "разделение по бутылочному горлышку" является не очень хорошим способом для кластеризации вершин в нашем датасете. </mark>

```{r}
# проводим кластеризацию при помощи метода Fast-greedy
cfg <- cluster_fast_greedy(net, weights=E(net)$weight) 

# смотрим на полученные в результате кластеризации объекты
mbship_cfg <- membership(cfg) 
# mbship_cfg

s_cfg <- sizes(cfg)
s_cfg

ms_cfg <- modularity(cfg)
ms_cfg # 0.5310055
```

```{r}
# cfg
```

```{r}
# > s_cfg <- sizes(cfg)
# > s_cfg
# Community sizes
#   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26 
# 219 144 212 132 141  94 189 120  84  82  28   3   2  15   3   3   2   2   2   2   2   2   2   2   2   2 
#  27  28  29  30  31  32  33  34  35  36 
#   2   2   2   2   2   2   2   2   2   2 
```

```{r}
# > ms_cfg <- modularity(cfg)
# > ms_cfg
# [1] 0.5310055
```

**Визуализация кластеризации методом Fast-greedy:**

```{r}
plot(
  cfg, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_nicely
)
```

```{r}
plot(
  cfg, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_with_lgl
)
```

```{r}
compare(cfg, V(net)$type, method='nmi') # 0.03386511
```

Таким образом, мы видим, что так же, как и предыдущий способ кластеризации, Fast-greedy не очень хорошо соответствует реальной классификации рассматриваемых институтов.

#### Выводы

**Вывод по Заданию 5:** Известные нам способы кластеризации (Edge-betweenness и Fast-greedy) не дали результата, похожего на имеющуюся в датасете классификацию.

------------------------------------------------------------------------

### Задание 6

Изначально был поставлен исследовательский вопрос, насколько активно при написании научных работ университеты Новой Зеландии взаимодействуют с другими типами организаций, нужно ли им как-то в этом способстовать извне (например, создавать общие лаботарии с индустриальными корпорациями и государственными органами). Помимо расчета значений гомофилии и различных видов центральностей, для ответа на заданный вопрос нам может помочь модель предсказания класса вершин *Relational Neighbors Classifier* (*RNC*).

Разделим все вершины на 2 класса: "1" - университет, "0" - иначе. Отберем из каждого класса по 10 вершин и положим вероятности их принадлежности первому классу соответственно `1` и `0`. Для всех остальных вершин (`unknown`) положим эту вероятность равной `0.5`. При каждой итерации будем обновлять вероятности каждой вершины исходя из вероятностей её соседей. В итоге, после 10 таких итераций получим для каждой вершины вероятность её принадлежности классу "1", и отберем те вершины, чья вероятность больше порога `0.5` в качестве принадлежащих классу "1".

Для избежания случайности повторим этот алгоритм 100 раз и построим гистограмму распределения числа предсказанных университетов, а также гистограмму распределения средних вероятностей принадлежности группе университетов.

```{r}
res <- rep(NA, 20)
pr <- rep(NA, 20)

for (j in 1:20){ 
  network <- net
  V(network)[which( V(network)$type == 'Higher Education' )]$type = 1
  V(network)[which(V(network)$type != 1)]$type = 0
  
  
  # вероятность вершины перейти в класс churn = 1 равна доле соседей churn = 1 от общего числа соседей
  # используем матричные вычисления
  random_uni <- sample( V(network)[ which(V(network)$type == 1) ], 10 )
  random_not_uni <- sample( V(network)[ which(V(network)$type == 0) ], 10 )
  
  
  for (i in 1:1511){
    if (!(V(network)[i] %in% random_uni | (V(network)[i] %in% random_not_uni))){
      V(network)$type[i] = 0.5
    }
  }
  
  UniProb <-  as.numeric(V(network)$type)
  threshold <- 0.5
  A <- as_adjacency_matrix(network)
  A <- as.matrix(A)
  Neighbors <- rowSums(A) # общее число соседей вершины
  
  UniProb_iter <- UniProb
  for(i in 1:10){
    UniProb_iter <- as.vector((A %*% UniProb_iter) / Neighbors)
  }
  res[j] <- length(which(UniProb_iter > threshold))
  pr[j] <- mean(UniProb_iter)
}
```

```{r}
hist(res, main='Число предсказанных университетов')
hist(pr, main='Средняя вероятность принадлежности классу 1')
```

Как можно увидеть, почти во всех случаях абсолютное число вершин предсказанj в качестве университетов. Получаем, что *какие бы 10 университетов мы ни взяли, их класс дойдет до большинства вершин быстрее, чем противоположный класс 10 случайных вершин*. Это распространяется и на случай, когда были выбраны наименее центральные университеты. Если бы университеты были плохо связаны с организациями другого типа, то их класс намного слабее распространялся бы на вершины другого типа, а это не так.

Значит, по крайней мере какие-то университеты (а именно наиболее центральные) довольно активно кооперируются с другими организациями (как, например, это делает Оклендский университет). Поэтому для таких университетов нет необходимости строить совместные с бизнесом и государством научные центры.

Вспомним про высокий показатель *dyadicity* у ВУЗов: выходит, что он получается таким большим из-за высокой гомофилии более мелких учебных заведений. Тогда можно предположить, что именно они плохо взаимодействуют с бизнесом и гос. органами.

------------------------------------------------------------------------

#### Заключение

Как тогда можно им помочь? При моделировании их класс распространялся по сети через их соседей --- крупные университеты. **В таком случае, более разумно строить научные центры именно соединяющие мелкие университеты с крупными. Данным образом, казалось бы, усиливая гомофилию, мы, наоборот, будем способстовать развитию научных отношений университетов с индустриальными партнерами.**

Замечание

:   Здесь мы предполагаем эталонность крупных университетов (например, Оклендского) с точки зрения эффективности взаимодействия, а также качества и количества научных работ, что продемонстрировано, например, в [этой статье](https://www.researchgate.net/publication/324091355_Why_Should_University_and_Business_Cooperate_A_Discussion_of_Advantages_and_Disadvantages).
